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Call number: | SPRINGER-2016-9783319239538:ONLINE Show nearby items on shelf |
Title: | Dynamics of a Quantum Spin Liquid |
Author(s): |
Johannes Knolle |
Date: | 2016 |
Size: | 1 online resource (4 p.) |
Note: | 10.1007/978-3-319-23953-8 |
Contents: | Introduction -- Kitaev's Honeycomb Lattice Model -- Dynamic Spin Correlations - Mapping to a Quantum Quench -- Results for the Structure Error -- Non-Abelian Phase and the Effect of Disorder -- Raman Scattering -- Conclusion and |
Outlook -- Appendix A: Pfaffians from Path Integrals -- Appendix B: X-Ray Edge and Singular Integral Equations -- Appendix C: Exact Diagonalization of Four Dimers -- Appendix D: Calculation of Matrix Elements | |
ISBN: | 9783319239538 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Quantum field theory , String theory , Superconductivity , Superconductors , Magnetism , Magnetic materials , Physics , Strongly Correlated Systems, Superconductivity , Magnetism, Magnetic Materials , Quantum Field Theories, String Theory |
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Call number: | SPRINGER-2016-9783319210186:ONLINE Show nearby items on shelf |
Title: | Integral Operators in Non-Standard Function Spaces Volume 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces |
Author(s): |
Vakhtang Kokilashvili |
Date: | 2016 |
Size: | 1 online resource (1003 p.) |
Note: | 10.1007/978-3-319-21018-6 |
Contents: | IV: Grand Lebesgue Spaces -- 14 Maximal Functions and Potentials -- 15 Grand Lebesgue Spaces on Sets with Infinite Measure -- V: Grand Morrey Spaces -- 16 Maximal Functions, Fractional and Singular Integrals -- 17 Multiple Operators on the Cone of Decreasing Functions -- A: Grand Bochner Spaces -- Bibliography -- Symbol Index -- Subject Index.IV: Grand Lebesgue Spaces -- 14 Maximal Functions and Potentials -- 15 Grand Lebesgue Spaces on Sets with Infinite Measure -- V: Grand Morrey Spaces -- 16 Max imal Functions, Fractional and Singular Integrals -- 17 Multiple Operators on the Cone of Decreasing Functions -- A: Grand Bochner Spaces -- Bibliography -- Symbol Index -- Subject Index |
ISBN: | 9783319210186 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications: 249 |
Keywords: | Mathematics , Functional analysis , Operator theory , Mathematics , Operator Theory , Functional Analysis |
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Call number: | SPRINGER-2016-9783319210155:ONLINE Show nearby items on shelf |
Title: | Integral Operators in Non-Standard Function Spaces Volume 1: Variable Exponent Lebesgue and Amalgam Spaces |
Author(s): |
Vakhtang Kokilashvili |
Date: | 2016 |
Size: | 1 online resource (567 p.) |
Note: | 10.1007/978-3-319-21015-5 |
Contents: | Preface -- I: Variable Exponent Lebesgue and Amalgam spaces -- 1 Hardy Type Operators -- 2 Oscillating weights -- 3 Kernel Integral Operators -- 4 Two-Weight Estimates -- 5 One-sided Operators -- 6 Two-weight Inequalities for Fractional Maximal Fun ctions -- 7 Hypersingular Integrals -- 8 Description of the Range of Potentials 213 -- 9 More on Compactness -- 10 Applications to Singular Integral Equations -- II: Hölder Spaces of Variable Order -- 11 Variable Order Hölder Spaces -- III: Variable Exp onent Morrey-Campanato and Herz Spaces -- 12 Morrey Type Spaces Constant Exponents -- 13 Morrey Type Spaces Variable Exponents -- Bibliography -- Symbol Index -- Subject Index |
ISBN: | 9783319210155 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications: 248 |
Keywords: | Mathematics , Functional analysis , Operator theory , Mathematics , Operator Theory , Functional Analysis |
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Call number: | SPRINGER-2014-9783319005966:ONLINE Show nearby items on shelf |
Title: | Analytic Capacity, the Cauchy Transform, and Non-homogeneous CaldernZygmund Theory [electronic resource] |
Author(s): |
Xavier Tolsa |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 19952005. The Cauchy transform plays a fundamental role in this areaand is accordingly one of t he main subjects covered. Another important topic, which may be of independent interest for many analysts, is the so-called non-homogeneous Caldern-Zygmund theory, the development of which has been largelymotivated by the problems arising in connection wi th analytic capacity. The Painlev problem, which was first posed around 1900, consists in finding a description of the removable singularities for bounded analytic functions in metricand geometric terms. Analytic capacity is a key tool in the study of thi s problem. In the 1960s Vitushkin conjectured that the removable sets which have finite length coincide with those which are purely unrectifiable. Moreover,because of the applications to the theory of uniform rational approximation, he posed the question as to whether analytic capacity is semiadditive. This work presents full proofs of Vitushkins conjecture and of the semiadditivity ofanalytic capacity, both of which remained open problems until very recently. Other related questions are also discussed, s uch as the relationship between rectifiability and the existence of principal values for the Cauchy transformsand other singular integrals. The book is largely self-contained and should be accessible for graduate students in analysis, as well as a valuabl e resource for researchers |
Contents: | Introduction |
Basic notation | |
Chapter 1. Analytic capacity | |
Chapter 2. Basic Caldern | |
Zygmund theory with non doubling measures | |
Chapter 3. The Cauchy transform and Menger curvature | |
Chapter 4. The capacity + | |
Chapter 5. A Tb theorem of Nazarov, Treil and Volberg | |
Chapter 6. The comparability between and +, and the semiadditivity of analytic capacity | |
Chapter 7. Curvature and rectifiability | |
Chapter 8. Principal values for the Cauchy transform and rectifiability | |
Chapter 9. RBMO() and H1 atb() | |
Bibliography | |
Index | |
ISBN: | 9783319005966 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Progress in Mathematics, 0743-1643 : v307 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Potential theory (Mathematics) , Mathematical optimization |
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Call number: | SPRINGER-2014-9783034808408:ONLINE Show nearby items on shelf |
Title: | Variable Lebesgue Spaces and Hyperbolic Systems [electronic resource] |
Author(s): |
David Cruz-Uribe Alberto Fiorenza Michael Ruzhansky Jens Wirth Sergey Tikhonov |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesguespaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integralswith non-standard growth conditions. They ha ve applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function spaceproperties of variable Lebesgue spaces proofs are modeled on the classic al theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such asconvolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolicequations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems withtime-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Ca uchy problems are constructed as oscillatory integrals by working in appropriatetime-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lo wer order terms can change asymptotic properties and thuscomplements the exposition |
Contents: | Part I: Introduction to the Variable Lebesgue Spaces |
Introduction and motivation | |
Properties of variable Lebesgue spaces | |
The Hardy | |
Littlewood maximal operator | |
Extrapolation in variable Lebesgue spaces | |
Part II:Asymptotic Behaviour of Solutions to Hyperbolic Equations and Systems | |
Equations with constant coefficients | |
Some interesting model cases | |
Time | |
dependent hyperbolic systems | |
Effective lower order perturbations | |
Examples and counter | |
examples | |
Related topics | |
ISBN: | 9783034808408 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Advanced Courses in Mathematics - CRM Barcelona, 2297-0304 : v27 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Differential equations, partial , Functions, special |
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Call number: | SPRINGER-2014-9783034808163:ONLINE Show nearby items on shelf |
Title: | Operator Theory, Operator Algebras and Applications [electronic resource] |
Author(s): |
M. Amlia Bastos Amarino Lebre Stefan Samko Ilya M Spitkovsky |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i)operator theory and ha rmonic analysis (singular integral operators with shifts pseudodifferential operators, factorization of almost periodic matrix functions inequalities Cauchy type integrals maximal and singular operators ongeneralized Orlicz-Morrey spaces the Riesz potenti al operator modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras inner endomorphisms of some semi group,crossed products C*-algebras generated by mappings which have finite orbits Foln er sequences in operator algebras arithmetic aspect of C*_r SL(2) C*-algebras of singular integral operators algebras of operator sequences) and (iii)mathematical physics (operator approach to diffraction from polygonal-conical screens Poisson geometry of difference Lax operators) |
Contents: | Flner Sequences in Operator Theory and Operator Algebras |
On the Factorization of Some Block Triangular Almost Periodic Matrix Functions | |
A C | |
algebra of Singular Integral Operators with Shifts Similar to Affine Mappings | |
On Cauchy Type Integrals Related to the Cimmino System of Partial Differential Equations | |
Singular Integral Operators with Linear Fractional Shifts on the Unit Circle | |
Diffraction from Polygonal | |
Conical Screens, An Operator Approach | |
Boundedness of the Maximal and Singular Operators on Generalized Orlicz | |
Morrey Spaces | |
On a Question by Markus Seidel | |
Inver | |
ISBN: | 9783034808163 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Operator Theory: Advances and Applications, 0255-0156 : v242 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034805483:ONLINE Show nearby items on shelf |
Title: | Variable Lebesgue Spaces [electronic resource] : Foundations and Harmonic Analysis |
Author(s): |
David V Cruz-Uribe Alberto Fiorenza |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They wereintroduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, andfor their applications to problems in physics and ima ge processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-onapproach that makes clear the similarities and differences between the vari able and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewoodmaximal operator is completely developed, and the connections between variable Lebesguespaces and t he weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Rieszpotentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolatio n from the theory of weighted norm inequalities. The final chapter applies the results from previouschapters to prove basic results about variable Sobolev spaces |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Structure of Variable Lebesgue Spaces | |
3 The Hardy | |
Littlewood Maximal Operator | |
4 Beyond Log | |
Hlder Continuity | |
5 Extrapolation in the Variable Lebesgue Spaces | |
6 Basic Properties of Variable Sobolev Spaces | |
Appendix: Open Problems | |
Bibliography | |
Symbol Index | |
Author Index | |
Subject Index. | |
ISBN: | 9783034805483 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Global analysis |
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Call number: | SPRINGER-2013-9783034805162:ONLINE Show nearby items on shelf |
Title: | Advances in Harmonic Analysis and Operator Theory [electronic resource] : The Stefan Samko Anniversary Volume |
Author(s): |
Alexandre Almeida Lus Castro Frank-Olme Speck |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attentionispaidto fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well asrelatedapplications, to mention but a few. Most of the contributions were originally presented at two conferences in Lisbon and Aveiro, Portugal, in JuneJuly 2011 |
Note: | Springer eBooks |
ISBN: | 9783034805162 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v229 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Operator theory , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9783034804691:ONLINE Show nearby items on shelf |
Title: | Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals [electronic resource] |
Author(s): |
Sergey Kislyakov Natan Kruglyak |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory. Theconstructions are based on far-reaching refinements of the classical CaldernZygmund decomposition. These new CaldernZygmund decompositions in turn are produced with the help of new covering theorems that combine manyremarkable features of classical resultsestablished byBesicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain near-minimizers) under the action of CaldernZygmund singularintegral operators. The book is divided into two parts. While the new method is presented in gre at detail in the second part, the first is mainly devoted to the prerequisites needed for a self-contained presentation of the main topic.There we discuss the classical covering results mentioned above, various spectacular applications of the classical Ca ldernZygmund decompositions, and the relationship of all this to real interpolation. It also serves as a quickintroduction to such important topics as spaces of smooth functions or singular integrals |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Definitions, notation, and some standard facts | |
Part 1. Background | |
Chapter 1. Classical CaldernZygmund decomposition and real interpolation | |
Chapter 2. Singular integrals | |
Chapter 3. Classical covering theorems | |
Chapter 4. Spaces of smooth functions and operators on them | |
Chapter 5. Some topics in interpolation | |
Chapter 6. Regularization for Banach spaces | |
Chapter 7. Stability for analytic Hardy spaces | |
Part 2. Advanced theory | |
Chapter 8. Controlled coverings | |
Chapter 9. Construction of near | |
minimizers | |
Chapter 10. Stability of near | |
mini | |
ISBN: | 9783034804691 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monografie Matematyczne : v74 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Call number: | SPRINGER-2013-9780817684006:ONLINE Show nearby items on shelf |
Title: | Further Developments in Fractals and Related Fields [electronic resource] : Mathematical Foundations and Connections |
Author(s): |
Julien Barral Stphane Seuret |
Date: | 2013 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, Fractals and Related Fields II, held in June 2011. The book provides readers with anoverview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fieldsrelated to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further Developments in Fractals and Related Fields is aimed at pure andapplied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenuesfor further research |
Note: | Springer eBooks |
Contents: | The Rauzy Gasket |
On the Hausdorff Dimension of Graphs ofPrevalent Continuous Functions on Compact Sets | |
Hausdorff Dimension and Diophantine Approximation | |
Singular Integrals on Self | |
Similar Subsets ofMetric Groups | |
Multivariate Davenport Series | |
Dimensions of Self | |
Affine Sets | |
The Multifractal Spectra of V | |
Statistics | |
Projections of Measures Invariant Under theGeodesic Flow | |
Multifractal Tubes | |
The Multiplicative Golden Mean Shift has Infinite Hausdorff Measure | |
The Law of Iterated Logarithm and Equilibrium Measures Versus Hausdorff Measures For Dynamically Semi | |
Regu | |
ISBN: | 9780817684006 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Differentiable dynamical systems , Functional analysis , Differential equations, partial , Geometry , Distribution (Probability theory) |
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Call number: | SPRINGER-2012-9780817683436:ONLINE Show nearby items on shelf |
Title: | Singularities of Differentiable Maps, Volume 2 [electronic resource] : Monodromy and Asymptotics of Integrals |
Author(s): |
V.I Arnold S.M Gusein-Zade A.N Varchenko |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Originally published inthe 1980s, Singularities of DifferentiableMaps: Monodromy and Asymptotics of Integrals was thesecond oftwovolumes that togetherformed a translation of the authors'influential Russian monographon singularity theory.This uncorrec ted softcover reprint of the work brings its still-relevant content back into the literature, making it availableand affordableto a global audience of researchers and practitioners. Whilethe first volume of this title, subtitled Classification of Critical Points, Caustics and Wave Fronts, contained the zoology of differentiable mapsthat is, was devoted to a description of what, where, and how singularities could beencounteredthis second volume concentrates on elements of theanatomy and physiology of singu larities of differentiable functions. The questions considered here are about the structure of singularities and how they function. Inthe first part the authors consider the topological structure of isolated critical points of holomorphic functions: vanis hing cycles distinguished bases intersection matricesmonodromy groupsthe variation operatorand theirinterconnections and method of calculation. The second part is devoted to the study of the asymptotic behavior of integrals of the method of stationary pha se, which is widely met within applications. The third and last part dealswith integrals evaluated over level manifolds in a neighborhood of the critical point of a holomorphic function. Thismonograph is suitablefor mathematicians, researchers, postgradua tes, and specialists in the areas ofmechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps |
Note: | Springer eBooks |
Contents: | Part I. The topological structure of isolated critical points of functions |
Introduction | |
Elements of the theory of Picard | |
Lefschetz | |
The topology of the non | |
singular level set and the variation operator of a singularity | |
The bifurcation sets and the monodromy group of a singularity | |
The intersection matrices of singularities of functions of two variables | |
The intersection forms of boundary singularities and the topology of complete intersections | |
Part II. Oscillatory integrals | |
Discussion of results | |
Elementary integrals and the resolution of singularities of the phase | |
As | |
ISBN: | 9780817683436 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2012-9780817683405:ONLINE Show nearby items on shelf |
Title: | Singularities of Differentiable Maps, Volume 1 [electronic resource] : Classification of Critical Points, Caustics and Wave Fronts |
Author(s): |
V.I Arnold S.M Gusein-Zade A.N Varchenko |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Originally published inthe 1980s, Singularities of DifferentiableMaps: The Classificationof Critical Points, Caustics and Wave Fronts was the first oftwovolumes that togetherformed a translation of theauthors'influential Russian monograph on singular ity theory.This uncorrected softcover reprint of the work brings its still-relevant content back into the literature, making it availableand affordableto a global audience ofresearchers and practitioners. Singularity theory isa far-reaching extension of m axima and minima investigations of differentiable functions, withimplications for many different areas of mathematics, engineering (catastrophe theoryand the theory of bifurcations), and science. The three parts of this first volume deal with the stabilit y problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. Building onthese concepts, the second volume (Monodromy and Asymptotics of Integrals) describes the topological and algebro-geometrical aspects of the theory, including monodromy, intersection forms, oscillatory integrals, asymptotics, and mixedHodge structures of singularities. Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts accommodates the needs of non-mathematicians,presupposing a limited mathematical background andbeginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explorean unparalleled breadth ofapplications |
Note: | Springer eBooks |
Contents: | Part I. Basic concepts |
The simplest examples | |
The classes Sigma^ I | |
The quadratic differential of a map | |
The local algebra of a map and the Weierstrass preparation theorem | |
The local multiplicity of a holomorphic map | |
Stability and infinitesimal stability | |
The proof of the stability theorem | |
Versal deformations | |
The classification of stable germs by genotype | |
Review of further results | |
Part II. Critical points of smooth functions | |
A start to the classification of critical points | |
Quasihomogeneous and semiquasihomogeneous singularities | |
The classification of quasih | |
ISBN: | 9780817683405 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2011-9781461405894:ONLINE Show nearby items on shelf |
Title: | Approximation by Multivariate Singular Integrals [electronic resource] |
Author(s): |
George A Anastassiou |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the generalmultivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly.This book studies the rate of convergence of these o perators to the unit operator as well as the related simultaneous approximation. The last chapter, which includes many examples, presents a related Korovkin type approximation theoremfor functions of two variables. Relevant background information and mot ivation is included in this exposition, and as a result this book can be used as supplementary text for several advanced courses. The results presented apply tomany areas of pure and applied mathematics, such a mathematical analysis, probability, statisti cs and partial differential equations. This book is appropriate for researchers and selected seminars at the graduate level |
Note: | Springer eBooks |
ISBN: | 9781461405894 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral Transforms , Differential equations, partial , Distribution (Probability theory) |
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Call number: | SPRINGER-2011-9780857296030:ONLINE Show nearby items on shelf |
Title: | Singularities of integrals [electronic resource] : Homology, hyperfunctions and microlocal analysis |
Author(s): |
Frdric Pham |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Bringing together two fundamental texts from Frdric Phams research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Usingnotions developed by J. Leray i n the calculus of residues in several variables and R. Thoms isotopy theorems, Frdric Phams foundational study of the singularities of integrals lies at the interface between analysis andalgebraic geometry, culminating in the Picard-Lefschetz formulae. Th ese mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from thepoint of view of hyperfunction theory and microlocal analysis. Providing a must-have introduc tion to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. Thisbook will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frdr ic Pham, now retired, was Professor at the University of Nice. He has published several educational and researchtexts. His recent work concerns semi-classical analysis and resurgent functions |
Note: | Springer eBooks |
Contents: | Differentiable manifolds |
Homology and cohomology of manifolds | |
Lerays theory of residues | |
Thoms isotopy theorem | |
Ramification around Landau varieties | |
Analyticity of an integral depending on a parameter | |
Ramification of an integral whose integrand is itself ramified | |
Functions of a complex variable in the Nilsson class | |
Functions in the Nilsson class on a complex analytic manifold | |
Analyticity of integrals depending on parameters | |
Sketch of a proof of Nilssons theorem | |
Examples: how to analyze integrals with singular integrands | |
Hyperfunctions in one variable, | |
ISBN: | 9780857296030 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial |
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Call number: | SPRINGER-2011-9780817647919:ONLINE Show nearby items on shelf |
Title: | A Modern Approach to Functional Integration [electronic resource] |
Author(s): |
John R Klauder |
Date: | 2011 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
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Note: | This text takes advantage of recent developments in the theory of path integration to provide an improved treatment of quantization of systems that either have no constraints or instead involve constraints with demonstrativelyimproved procedures. Str ong emphasis is placed on the coherent state form of the path integral, which typically is only briefly mentioned in the textbook literature. Also of prime importance, a key focus of the book will be on theprojection operator method of enforcing quantum c onstraints. Additionally, several novel proposals are introduced to deal with highly singular quantum field theories. The modern treatment used by the author is an attempt to make amajor paradigm shift in how the art of functional integration is practiced . The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and appliedmathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. Ke y topics and features: * A thorough grounding in the Gold Standard of path integrals: the Wiener measure * Formulation of all pathintegral construction from abstract principles * A review of coherent state fundamentals * A critical comparison of several p ath integral versions with emphasis on the virtues of the coherent state version * A construction of theWiener-measure regularized phase space path integral, its emergence as a coherent state path integral, and its superior definition and connection to th e classical theory underlying the quantization * A review of classical and quantumconstraints and some of their traditional treatments * Introduction of the projection operator method to deal with quantum constraints, its many virtues as compared to tradi tional methods, and how it can be incorporated into aconventional or coherent state phase space path integral * An extension of the books principal discussion into the realm of quantum field theory w |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Part I: Stochastic Theory | |
Probability | |
Infinite | |
Dimensional Integrals | |
Stochastic Variable Theory | |
Part II: Quantum Theory | |
Background to an Analysis of Quantum Mechanics | |
Quantum Mechanical Path Integrals | |
Coherent State Path Integrals | |
Continuous | |
Time Regularized Path Integrals | |
Classical and Quantum Constraints | |
Part III: Quantum Field Theory | |
Application to Quantum Field Theory | |
A Modern Approach to Nonrenormalizable Models | |
References | |
Index | |
ISBN: | 9780817647919 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Differential equations, partial , Quantum theory |
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Call number: | SPRINGER-2009-9783642016776:ONLINE Show nearby items on shelf |
Title: | Boundary Value Problems and Markov Processes [electronic resource] |
Author(s): |
Kazuaki Taira |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
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Note: | This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, aMarkovian particle in a doma in of Euclidean space is governed by an integro-differential operator, called a Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel' boundary condition,on the boundary of the domain. Probabilistically, a Markovian particle moves both by jumps and continuously in the state space and it obeys the Ventcel' boundary condition, which consists of six terms corresponding to the diffusionalong the boundary, the absorption phenomenon, the reflection phenomenon, the sticking (or viscosity) phenomenon, the jump phenomenon on the boundary, and the inward jump phenomenon from the boundary. In particular, second-orderelliptic differential operators are called diffusion operators and describe analytically strong Mark ov processes with continuous paths in the state space such as Brownian motion. We observe that second-order elliptic differentialoperators with smooth coefficients arise naturally in connection with the problem of construction of Markov processes in proba bility. Since second-order elliptic differential operators are pseudo-differential operators, we can make useof the theory of pseudo-differential operators as in the previous book: Semigroups, boundary value problems and Markov processes (Springer-Verlag, 2004). Our approach here is distinguished by its extensive use of the ideas andtechniques characteristic of the recent developments in the theory of partial differential equations. Several recent developments in the theory of singular integrals have made further progress in the study of elliptic boundary valueproblems and hence in the study of Markov processes possible. The presentation of these new results is the main purpose of this book |
Note: | Springer eBooks |
Contents: | 1 Semigroup Theory |
2 Lp Theory of Pseudo | |
Differential Operators | |
3 Lp Approach to Elliptic Boundary Value Problems | |
4 Proof of Theorem 1 | |
5 A Priori Estimates | |
6 Proof of Theorem 2 | |
7 Proof of Theorem 3, Part (i) | |
8 Proof of Theorem 3, Part (ii) | |
9 Application to Semilinear Initial | |
Boundary Value Problems | |
ISBN: | 9783642016776 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1499 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Differential equations, partial , Distribution (Probability theory) |
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Call number: | SPRINGER-2009-9780817646691:ONLINE Show nearby items on shelf |
Title: | Explorations in Harmonic Analysis [electronic resource] : with Applications to Complex Function Theory and the Heisenberg Group |
Author(s): |
Steven G Krantz |
Date: | 2009 |
Edition: | 1 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novicemathematical reader fr om the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis. Within the textbook, the new ideas on the Heisenberg group areapplied to the study of estimates for both the Szeg and PoissonSzeg integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous butwell-paced exposition, this text provides all the necessary background in singul ar and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis.Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis |
Note: | Springer eBooks |
Contents: | Preface |
Background in Fourier Series | |
The Fourier Transform | |
Fractional and Singular Integrals | |
Pseudodifferential Operators | |
The Real Variable Point of View | |
Several Complex Variables | |
Canonical Integral Operators | |
Boundary Behavior | |
The Heisenberg Group | |
Analysis on the Heisenberg Group | |
Index | |
ISBN: | 9780817646691 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Harmonic analysis , Fourier analysis , Differential equations, partial |
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Call number: | SPRINGER-2009-9780817645885:ONLINE Show nearby items on shelf |
Title: | Recent Developments in Real and Harmonic Analysis [electronic resource] : In Honor of Carlos Segovia |
Author(s): |
Carlos Cabrelli Jose Luis Torrea |
Date: | 2009 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis. The work begins with a chronological description of Segoviasmathematical life, his origin al ideas and their evolution, which may be a source of inspiration for many mathematicians working in the fields of harmonic analysis, functional analysis, and partial differential equations. Apart fromthis contribution, two different types of chapters ar e featured in the work: surveys dealing with Carlos favorite topics, and PDE works written by students and colleagues close to Segovia whose careers were in some way influenced byhim. Specific topics covered include: * Vector-valued singular integral equa tions * Harmonic analysis related to Hermite expansions * Gas flow in porous media * Global well-posedness of the KPI Equation * MongeAmpre type equationsand applications * Spaces of homogeneous type * Hardy and Lipschitz spaces * One-sided operators This book will be useful to graduate students as well as pure and applied mathematicians interested in new mathematical developments inareas related to real and harmonic analysis. Contributors: H. Aimar, A. Bonami, O. Blasco, L.A. Caffarelli, S. Chanillo, J. Feuto, L. Forzani, C.E. Guterrez, E. Harboure, A.L. Karakhanyan, C.E. Kenig, R.A. Macas, J.J. Manfredi,F.J. Martn-Reyes, P. Ortega, R. Scotto, A. de la Torre, J.L. Torrea |
Note: | Springer eBooks |
Contents: | Carlos Segovia Fernndez |
Balls as Subspaces of Homogeneous Type: On a Construction due to R. Macas and C. Segovia | |
Some Aspects of Vector | |
Valued Singular Integrals | |
Products of Functions in Hardy and Lipschitz or BMO Spaces | |
Harmonic Analysis Related to Hermite Expansions | |
Weights for OneSided Operators | |
Lectures on Gas Flow in Porous Media | |
Sharp Global Bounds for the Hessian on Pseudo | |
Hermitian Manifolds | |
Recent Progress on the Global Well | |
Posedness of the KPI Equation | |
On MongeAmpre Type Equations and Applications | |
ISBN: | 9780817645885 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Harmonic analysis , Fourier analysis , Engineering mathematics |
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Call number: | SPRINGER-2009-9780387094342:ONLINE Show nearby items on shelf |
Title: | Modern Fourier Analysis [electronic resource] |
Author(s): |
Loukas Grafakos |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition ofnew material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation,Fourier Series, the Fourier Transform, Maximal Func tions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals ofNonconvolution Type, and Weighted Inequalities. These volumes are mainly addressed t o graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. Theprerequisites for the first volume are satisfactory completion of courses in real and complex variables. The s econd volume assumes material from the first. This book is intended to present the selected topics in depth and stimulatefurther study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of a nalysis on the torus. This material is included for historical reasons, as the genesis of Fourieranalysis can be found in trigonometric expansions of periodic functions in several variables. About the first edition: Grafakos's book is very user-friendly w ith numerous examples illustrating the definitions and ideas... Thetreatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises. - Kenneth Ross, MAA Online |
Note: | Springer eBooks |
Contents: | Smoothness and Function Spaces |
and Carleson Measures | |
Singular Integrals of Nonconvolution Type | |
Weighted Inequalities | |
Boundedness and Convergence of Fourier Integrals | |
Time Frequency Analysis and the CarlesonHunt Theorem | |
ISBN: | 9780387094342 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v250 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Functional analysis |
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Call number: | SPRINGER-2009-9780387094328:ONLINE Show nearby items on shelf |
Title: | Classical Fourier Analysis [electronic resource] |
Author(s): |
Loukas Grafakos |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition ofnew material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation,Fourier Series, the Fourier Transform, Maximal Func tions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals ofNonconvolution Type, and Weighted Inequalities. These volumes are mainly addressed t o graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. Theprerequisites for the first volume are satisfactory completion of courses in real and complex variables. The s econd volume assumes material from the first. This book is intended to present the selected topics in depth and stimulatefurther study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of a nalysis on the torus. This material is included for historical reasons, as the genesis of Fourieranalysis can be found in trigonometric expansions of periodic functions in several variables. About the first edition: Grafakos's book is very user-friendly w ith numerous examples illustrating the definitions and ideas... Thetreatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises. - Kenneth Ross, MAA Online |
Note: | Springer eBooks |
Contents: | Preface |
Lp Spaces and Interpolation | |
Maximal Functions, Fourier Transform, and Distributions | |
Fourier Analysis on the Torus | |
Singular Integrals of Convolution Type | |
Littlewood | |
Paley Theory and Multipliers | |
Gamma and Beta Functions | |
Bessel Functions | |
Rademacher Functions | |
Spherical Coordinates | |
Some Trigonometric Identities and Inequalities | |
Summation by Parts | |
Basic Functional Analysis | |
The Minimax Lemma | |
The Schur Lemma | |
The Whitney Decomposition of Open Sets in Rn | |
Smoothness and Vanishing Moments | |
Glossary | |
References | |
Index | |
ISBN: | 9780387094328 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v249 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Functional analysis |
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Call number: | SPRINGER-2008-9783540769569:ONLINE Show nearby items on shelf |
Title: | Mathematical Theory of Feynman Path Integrals [electronic resource] : An Introduction |
Author(s): |
Sergio A Albeverio Raphael J Hegh-Krohn Sonia Mazzucchi |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation,cosmology. Recently ideas bas ed on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis andgeometry, and number theory. The 2nd edition of LNM 523 i s based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire newchapter on the current forefront of research has been added. Except for this new ch apter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapterthe reader will also find notes with further bibliographical information |
Note: | Springer eBooks |
Contents: | Preface to the second edition |
Preface to the first edition | |
1.Introduction | |
2.The Fresnel Integral of Functions on a Separable Real Hilbert Spa | |
3.The Feynman Path Integral in Potential Scattering | |
4.The Fresnel Integral Relative to a Non | |
singular Quadratic Form | |
5.Feynman Path Integrals for the Anharmonic Oscillator | |
6.Expectations with Respect to the Ground State of the Harmonic Oscillator | |
7.Expectations with Respect to the Gibbs State of the Harmonic Oscillator | |
8.The Invariant Quasi | |
free States | |
9.The Feynman Hystory Integral for the Relativistic Quantum Boson Field | |
ISBN: | 9783540769569 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v523 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Global analysis , Operator theory , Distribution (Probability theory) , Quantum theory |
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Call number: | SPRINGER-2008-9783540745877:ONLINE Show nearby items on shelf |
Title: | Weighted Littlewood-Paley Theory and Exponential-Square Integrability [electronic resource] |
Author(s): |
Michael Wilson |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Littlewood-Paley theory is an essential tool of Fourier analysis, with applications and connections to PDEs, signal processing, and probability. It extends some of the benefits of orthogonality to situations where orthogonalitydoesnt really make sens e. It does so by letting us control certain oscillatory infinite series of functions in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could bemade much sharper than was previously suspected . The present book tries to give a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications |
Note: | Springer eBooks |
Contents: | Some Assumptions |
An Elementary Introduction | |
Exponential Square | |
Many Dimensions Smoothing | |
The Caldern Reproducing Formula I | |
The Caldern Reproducing Formula II | |
The Caldern Reproducing Formula III | |
Schrdinger Operators | |
Some Singular Integrals | |
Orlicz Spaces | |
Goodbye to Good | |
? | |
A Fourier Multiplier Theorem | |
Vector | |
Valued Inequalities | |
Random Pointwise Errors | |
ISBN: | 9783540745877 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1924 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Differential equations, partial |
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Call number: | SPRINGER-2006-9780387245362:ONLINE Show nearby items on shelf |
Title: | Real and Complex Clifford Analysis [electronic resource] |
Author(s): |
Sha Huang Yu Ying Qiao Guo Chun Wen |
Date: | 2006 |
Publisher: | Boston, MA : Springer US |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications. In this book, the authors introduce many properties of regular functions andgeneralized regular functions i n real Clifford analysis, as well as harmonic functions in complex Clifford analysis. It covers important developments in handling the incommutativity of multiplication in Clifford algebra, thedefinitions and computations of high-order singular integrals, boundary value problems, and so on. In addition, the book considers harmonic analysis and boundary value problems in four kinds of characteristic fields proposed by LuogengHua for complex analysis of several variables. The great majority of the contents originate in the authors investigations, and this new monograph will be interesting for researchers studying the theory of functions. Audience Thisbook is intended for mathematicians studying function theory |
Note: | Springer eBooks |
Contents: | General Regular and Harmonic Functions in Real and Complex Clifford Analysis |
Boundary Value Problems of Generalized Regular Functions and Hyperbolic Harmonic Functions in Real Clifford Analysis | |
Nonlinear Boundary Value Problems for Generalized Biregular Functions in Real Clifford Analysis | |
Boundary Value Problems of Second Order Partial Differential Equations for Classical Domains in Real Clifford Analysis | |
Integrals Dependent on Parameters and Singular Integral Equations in Real Clifford Analysis | |
Several Kinds of High Order Singular Integrals and Differential Integral Equations i | |
ISBN: | 9780387245362 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Advances in Complex Analysis and Its Applications : v5 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Integral equations , Differential equations, partial |
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Call number: | SPRINGER-2005-9783764373450:ONLINE Show nearby items on shelf |
Title: | Isomorphisms between H1 Spaces [electronic resource] |
Author(s): |
Paul F.X Mller |
Date: | 2005 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This book presents a thorough and self-contained presentation of H and its known isomorphic invariants, such as the uniform approximation property, the dimension conjecture, and dichotomies for the complemented subspaces. Thenecessary background is d eveloped from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it (averaging projections, rearrangement operators, paraproducts,Calderon-Zygmund singular integrals). Complete proofs are gi ven for the classical martingale inequalities of C. Fefferman, Burkholder, and Khinchine-Kahane, and for large deviation inequalities. Complex interpolation, analytic familiesof operators, and the Calderon product of Banach lattices are treated in the con text of H^p spaces. Througout the book, special attention is given to the combinatorial methods developed in the field, particularly J. Bourgain's proof ofthe dimension conjecture, L. Carleson's biorthogonal system in H, T. Figiel's integral representatio n, W.B. Johnson's factorization of operators, B. Maurey's isomorphism, and P. Jones' proof of the uniform approximation property. Anentire chapter is devoted to the study of combinatorics of colored dyadic intervals |
Note: | Springer eBooks |
Contents: | Preface |
1. The Haar System: Basic Facts and Classical results | |
2. Projections, Isomorphisms, and Interpolation | |
3. Combinatorics of Colored Dyadic Intervals | |
4. Martingale H^1 Spaces | |
5. Isomorphic Invariants for H^1 | |
6. Atomic H^1 Spaces | |
Bibliography | |
List of Symbols | |
Index | |
ISBN: | 9783764373450 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN) : v66 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Harmonic analysis , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2005-9780387283135:ONLINE Show nearby items on shelf |
Title: | Methods and Applications of Singular Perturbations [electronic resource] : Boundary Layers and Multiple Timescale Dynamics |
Author(s): |
Ferdinand Verhulst |
Date: | 2005 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this uniquebook deliniates boun dary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in thecontext of the general theory, as well as a final discussion of the more advanced problems. Precise estimates and excursions into the theoretical background makes this workbook valuable to both the applied sciences and mathematicsfields. As a bonus in its last chapter the book includes a collecti on of rare and useful pieces of literature, such as the summary of the Perturbation theory of Matrices. Detailed illustrations, stimulating examples and exercises aswell as a clear explanation of the underlying theory makes this workbook ideal for senior undergraduate and beginning graduate students in applied mathematics as well as science and engineering fields |
Note: | Springer eBooks |
Contents: | From the contents: Introduction |
Basic material | |
Approximation of integrals | |
Boundary layer behaviour | |
Two | |
point boundary value problems | |
Nonlinear boundary | |
value problems | |
Elliptic boundary value problems | |
Boundary layers in time | |
Evolution equations with boundary layers | |
The continuation method | |
Averaging and timescales | |
Advanced averaging | |
Averaging for evolution equations | |
Wave equations on unbounded domains | |
Appendices. Epilogue. Answers to Odd | |
Numbered Exercises. Literature. Index | |
ISBN: | 9780387283135 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Texts in Applied Mathematics, 0939-2475 : v50 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Differential Equations , Differential equations, partial , Numerical analysis , Mathematical physics |
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Call number: | SPRINGER-2004-9783034879118:ONLINE Show nearby items on shelf |
Title: | Limit Operators and Their Applications in Operator Theory |
Author(s): |
Vladimir Rabinovich |
Date: | 2004 |
Size: | 1 online resource (392 p.) |
Note: | 10.1007/978-3-0348-7911-8 |
Contents: | 1 Limit Operators -- 1.1 Generalized compactness, generalized convergence -- 1.2 Limit operators -- 1.3 Algebraization -- 1.4 Comments and references -- 2 Fredholmness of Band-dominated Operators -- 2.1 Band-dominated operators -- 2.2 |
P-Fredholmness of rich band-dominated operators -- 2.3 Local P-Fredholmness: elementary theory -- 2.4 Local P-Fredholmness: advanced theory -- 2.5 Operators in the discrete Wiener algebra -- 2.6 Band-dominated operators with special | |
coefficients -- 2.7 Indices of Fredholm band-dominated operators -- 2.8 Comments and references -- 3 Convolution Type Operators on $${\mathbb{R}^N}$$ -- 3.1 Band-dominated operators on $${L^p}\left( {{\mathbb{R}^N}} \right)$$ -- 3.2 | |
Operators of convolution -- 3.3 Fredholmness of convolution type operators -- 3.4 Compressions of convolution type operators -- 3.5 A Wiener algebra of convolution-type operators -- 3.6 Comments and references -- 4 Pseudodifferential | |
Operators -- 4.1 Generalities and notation -- 4.2 Bi-discretization of operators on $${L^2}\left( {{\mathbb{R}^N}} \right)$$ -- 4.3 Fredholmness of pseudodifferential operators -- 4.4 Applications -- 4.5 Mellin pseudodifferential | |
operators -- 4.6 Singular integrals over Carleson curves with Muckenhoupt weights -- 4.7 Comments and references -- 5 Pseudodifference Operators -- 5.1 Pseudodifference operators -- 5.2 Fredholmness of pseudodifference operators -- 5.3 | |
Fredholm properties of pseudodifference operators on weighted spaces -- 5.4 Slowly oscillating pseudodifference operators -- 5.5 Almost periodic pseudodifference operators -- 5.6 Periodic pseudodifference operators -- 5.7 Semi-periodic | |
pseudodifference operators -- 5.8 Discrete Schrödinger operators -- 5.9 Comments and references -- 6 Finite Sections of Band-dominated Operators -- 6.1 Stability of the finite section method -- 6.2 Finite sections of band-dominated | |
operators on $${\mathbb{Z}^1}$$ and $${\mathbb{Z}^2}$$ -- 6.3 Spectral approximation -- 6.4 Fractality of approximation methods -- 6.5 Comments and references -- 7 Axiomatization of the Limit Operators Approach -- 7.1 An axiomatic | |
approach to the limit operators method -- 7.2 Operators on homogeneous groups -- 7.3 Fredholm criteria for convolution type operators with shift -- 7.4 Comments and references | |
ISBN: | 9783034879118 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications : 150 |
Keywords: | Mathematics , Operator theory , Mathematics , Operator Theory |
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Call number: | SPRINGER-2004-9781461220541:ONLINE Show nearby items on shelf |
Title: | Real and Stochastic Analysis New Perspectives |
Author(s): | |
Date: | 2004 |
Size: | 1 online resource (406 p.) |
Note: | 10.1007/978-1-4612-2054-1 |
Contents: | and Outline -- References -- Stochastic Differential Equations and Hypoelliptic Operators -- 1 Introduction -- 2 Integration by parts and the regularity of induced measures -- 3 A Hörmander theorem for infinitely degenerate operators |
-- 4 A study of a class of degenerate functional stochastic differential equations -- 5 Some open problems -- References -- Curved Wiener Space Analysis -- 1 Introduction -- 2 Manifold primer -- 3 Riemannian geometry primer -- 4 Flows | |
and Cartan's development map -- 5 Stochastic calculus on manifolds -- 6 Heat kernel derivative formula -- 7 Calculus on W(M) -- 8 Malliavin's methods for hypoelliptic operators -- 9 Appendix: Martingale and SDE estimates -- References | |
-- Noncommutative Probability and Applications -- 1 Introduction -- 2 Traditional probability theory -- 3 Unsharp traditional probability theory -- 4 Sharp quantum probability -- 5 Unsharp quantum probability -- 6 Effects and | |
observables -- 7 Statistical maps -- 8 Sequential products on Hilbert space -- 9 Quantum operations -- 10 Completely positive maps -- 11 Sequential effect algebras -- 12 Further SEA results -- References -- Advances and Applications of | |
the Feynman Integral -- 1 Introduction -- 2 The operator valued Feynman integral -- 3 Evolution processes -- 4 The Feynman-Kac formula -- 5 Boundedness of processes -- 6 Path integrals on finite sets -- 7 The Dirac equation in one | |
space dimension -- 8 Integration with respect to unbounded set functions -- 9 The Feynman integral with singular potentials -- 10 Quantum field theory -- References -- Stochastic Differential Equations Based on Lévy Processes and | |
Stochastic Flows of Diffeomorphisms -- 1 Stochastic integrals for sernimartingales -- 2 Stochastic analysis of Lévy processes -- 3 Stochastic differential equation and stochastic flow -- 4 Appendix. Kolmogorov's criterion for the | |
continuity of random fields and the uniform convergence of random fields -- References -- Convolutions of Vector Fields-III: Amenability and Spectral Properties -- 1 Introduction -- 2 Elementary Aspects of Random Walks -- 3 Role of the | |
Spectrum of Convolution Operators -- 4 Amenable Function Algebras and Groups -- 5 Spectra of Convolution Operators and Amenability -- 6 Beurling and Segal Algebras for Amenability -- References | |
ISBN: | 9781461220541 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Functional analysis , Partial differential equations , Probabilities , Statistics , Mathematics , Analysis , Probability Theory and Stochastic Processes , Functional Analysis , Partial Differential Equations , Statistical Theory and Methods |
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Call number: | SPRINGER-2004-9780817681982:ONLINE Show nearby items on shelf |
Title: | Methods of Applied Mathematics with a MATLAB Overview |
Author(s): |
Jon H Davis |
Date: | 2004 |
Size: | 1 online resource (721 p.) |
Note: | 10.1007/978-0-8176-8198-2 |
Contents: | 1 Introduction -- 1.1 An Overview -- 1.2 Topics by Chapter -- 1.3 Applying Mathematics -- References -- 2 Fourier Series -- 2.1 Introduction -- 2.2 Inner Products and Fourier Expansions -- 2.3 Convergence of Fourier Series -- 2.4 |
Pointwise and Uniform Convergence of Fourier Series -- 2.5 Gibb’s Phenomenon and Summation Methods -- 2.6 Summation Methods -- 2.7 Fourier Series Properties -- 2.8 Periodic Solutions of Differential Equations -- 2.9 Impedance Methods | |
and Periodic Solutions -- 2.10 Power Spectrum and Parseval’s Theorem -- References -- 3 Elementary Boundary Value Problems -- 3.1 Introduction -- 3.2 The One-Dimensional Diffusion Equation -- 3.3 The Wave Equation -- 3.4 The Potential | |
Equation -- 3.5 Discrete Models of Boundary Value Problems -- 3.6 Separation of Variables -- 3.7 Half-Range Expansions and Symmetries -- 3.8 Some Matters of Detail -- References -- 4 Sturm-Liouville Theory and Boundary Value Problems | |
-- 4.1 Further Boundary Value Problems -- 4.2 Selfadjoint Eigenvalue Problems -- 4.3 Sturm-Liouville Problems -- 4.4 Power Series and Singular Sturm-Liouville Problems -- 4.5 Cylindrical Problems and Bessel’s Equation -- 4.6 | |
Multidimensional Problems and Forced Systems -- 4.7 Finite Differences and Numerical Methods -- 4.8 Variational Models and Finite Element Methods -- 4.9 Computational Finite Element Methods -- References -- 5 Functions of a Complex | |
Variable -- 5.1 Complex Variables and Analytic Functions -- 5.2 Domains of Definition of Complex Functions -- 5.3 Integrals and Cauchy’s Theorem -- 5.4 Cauchy’s Integral Formula, Taylor Series, and Residues -- 5.5 Complex Variables and | |
Fluid Flows -- 5.6 Conformal Mappings and the Principle of the Argument -- References -- 6 Laplace Transforms -- 6.1 Introduction -- 6.2 Definitions of the Laplace Transform -- 6.3 Mechanical Properties of Laplace Transforms -- 6.4 | |
Elementary Transforms and Fourier Series Calculations -- 6.5 Elementary Applications to Differential Equations -- 6.6 Convolutions, Impulse Responses, and Weighting Patterns -- 6.7 Vector Differential Equations -- 6.8 Impedance Methods | |
-- References -- 7. Fourier Transforms -- 7.1 Introduction -- 7.2 Basic Fourier Transforms -- 7.3 Formal Properties of Fourier Transforms -- 7.4 Convolutions and Parseval’s Theorem -- 7.5 Comments on the Inversion Theorem -- 7.6 | |
Fourier Inversion by Contour Integration -- 7.7 The Laplace Transform Inversion Integral -- 7.8 An Introduction to Generalized Functions -- 7.9 Fourier Transforms, Differential Equations and Circuits -- 7.10 Transform Solutions of | |
Boundary Value Problems -- 7.11 Band-limited Functions and Communications -- References -- 8 Discrete Variable Transforms -- 8.1 Some Discrete Variable Models -- 8.2 Z-Transforms -- 8.3 Z-Transform Properties -- 8.4 z-Transform | |
Inversion Integral -- 8.5 Discrete Fourier Transforms -- 8.6 Discrete Fourier Transform Properties -- 8.7 Some Applications of Discrete Transform Methods -- 8.8 Finite and Fast Fourier Transforms -- 8.9 Finite Fourier Properties -- | |
8.10 Fast Finite Transform Algorithm -- 8.11 Computing The 1-1.1 -- References -- 9 Additional Topics -- 9.1 Local Waveform Analysis -- 9.2 Uncertainty Principle -- 9.3 Short-Time Fourier Transforms -- 9.4 Function Shifts and Scalings | |
-- 9.5 Orthonormal Shifts -- 9.6 Multi-Resolution Analysis and Wavelets -- 9.7 On Wavelet Applications -- 9.8 Two-Sided Transforms -- 9.9 Walsh Functions -- 9.10 Geometrically Based Transforms -- References -- A Linear Algebra Overview | |
-- A.1 Vector spaces -- A.2 Linear Mappings -- A.3 Inner Products -- A.4 Linear Functionals and Dual Spaces -- A.5 Canonical Forms -- References -- B Software Resources -- B.1 Computational and Visualization Software -- B.2 MATLAB Data | |
Structures -- B.3 MATLAB Operators and Syntax -- B.4 MATLAB Programming Structures -- B.5 MATLAB Programs and Scripts -- B.6 Common Idioms -- B.7 Graphics -- B.8 Toolboxes and Enhancemants -- References -- C Transform Tables -- C.1 | |
Laplace Transforms -- C.2 Fourier Transforms -- C.3 Z Transforms -- C.4 Discrete Fourier Transforms | |
ISBN: | 9780817681982 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Functions of complex variables , Applied mathematics , Engineering mathematics , Computer mathematics , Physics , Mathematics , Fourier Analysis , Computational Mathematics and Numerical Analysis , Theoretical, Mathematical and Computational Physics , Applications of Mathematics , Abstract Harmonic Analysis , Functions of a Complex Variable |
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Call number: | SPRINGER-2003-9783662132425:ONLINE Show nearby items on shelf |
Title: | Two-Scale Stochastic Systems Asymptotic Analysis and Control |
Author(s): |
Yuri Kabanov |
Date: | 2003 |
Size: | 1 online resource (266 p.) |
Note: | 10.1007/978-3-662-13242-5 |
Contents: | 0 Warm-up -- 1 Toolbox: Moment Bounds for Solutions of Stable SDEs -- 2 The Tikhonov Theory for SDEs -- 3 Large Deviations -- 4 Uniform Expansions for Two-Scale Systems -- 5 Two-Scale Optimal Control Problems -- 6 Applications -- A.1 |
Basic Facts About SDEs -- A.1.1 Existence and Uniqueness of Strong Solutions for SDEs with Random Coefficients -- A.1.2 Existence and Uniqueness with a Lyapunov Function -- A.1.3 Moment Bounds for Linear SDEs -- A.1.4 The Novikov | |
Condition -- A.2 Exponential Bounds for Fundamental Matrices -- A.2.1 Uniform Bound in the Time-Homogeneous Case -- A.2.2 Nonhomogeneous Case -- A.2.3 Models with Singular Perturbations -- A.3 Total Variation Distance and Hellinger | |
Processes -- A.3.1 Total Variation Distance and Hellinger Integrals -- A.3.2 The Hellinger Processes -- A.3.3 Example: Diffusion-Type Processes -- A.4 Hausdorff Metric -- A.5 Measurable Selection -- A.5.1 Aumann Theorem -- A.5.2 | |
Filippov Implicit Function Lemma -- A.5.3 Measurable Version of the Carathéodory Theorem -- A.6.1 Notations and Preliminaries -- A.6.2 Integration of Stochastic Kernels -- A.6.3 Distributions of Integrals -- A.6.4 Compactness of the | |
Limit of Attainability Sets -- A.6.5 Supports of Conditional Distributions -- A.7 The Komlós Theorem -- Historical Notes -- References | |
ISBN: | 9783662132425 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Applications of Mathematics, Stochastic Modelling and Applied Probability: 49 |
Keywords: | Mathematics , System theory , Probabilities , Mathematics , Probability Theory and Stochastic Processes , Systems Theory, Control |
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Call number: | SPRINGER-2003-9780387215846:ONLINE Show nearby items on shelf |
Title: | Numerical Analysis in Modern Scientific Computing An Introduction |
Author(s): |
Peter Deuflhard |
Date: | 2003 |
Edition: | Second Edition |
Size: | 1 online resource (340 p.) |
Note: | 10.1007/978-0-387-21584-6 |
Contents: | 1 Linear Systems -- 1.1 Solution of Triangular Systems -- 1.2 Gaussian Elimination -- 1.3 Pivoting Strategies and Iterative Refinement -- 1.4 Cholesky Decomposition for Symmetric Positive Definite Matrices -- Exercises -- 2 Error |
Analysis -- 2.1 Sources of Errors -- 2.2 Condition of Problems -- 2.3 Stability of Algorithms -- 2.4 Application to Linear Systems -- Exercises -- 3 Linear Least-Squares Problems -- 3.1 Least-Squares Method of Gauss -- 3.2 | |
Orthogonalization Methods -- 3.3 Generalized Inverses -- Exercises -- 4 Nonlinear Systems and Least-Squares Problems -- 4.1 Fixed-Point Iterations -- 4.2 Newton Methods for Nonlinear Systems -- 4.3 Gauss-Newton Method for Nonlinear | |
Least-Squares Problems -- 4.4 Nonlinear Systems Depending on Parameters -- Exercises -- 5 Linear Eigenvalue Problems -- 5.1 Condition of General Eigenvalue Problems -- 5.2 Power Method -- 5.3 QR-Algorithm for Symmetric Eigenvalue | |
Problems -- 5.4 Singular Value Decomposition -- 5.5 Stochastic Eigenvalue Problems -- Exercises -- 6 Three-Term Recurrence Relations -- 6.1 Theoretical Background -- 6.2 Numerical Aspects -- 6.3 Adjoint Summation -- Exercises -- 7 | |
Interpolation and Approximation -- 7.1 Classical Polynomial Interpolation -- 7.2 Trigonometric Interpolation -- 7.3 Bézier Techniques -- 7.4 Splines -- Exercises -- 8 Large Symmetric Systems of Equations and Eigenvalue Problems -- 8.1 | |
Classical Iteration Methods -- 8.2 Chebyshev Acceleration -- 8.3 Method of Conjugate Gradients -- 8.4 Preconditioning -- 8.5 Lanczos Methods -- Exercises -- 9 Definite Integrals -- 9.1 Quadrature Formulas -- 9.2 Newton-Cotes Formulas | |
-- 9.3 Gauss-Christoffel Quadrature -- 9.4 Classical Romberg Quadrature -- 9.5 Adaptive Romberg Quadrature -- 9.6 Hard Integration Problems -- 9.7 Adaptive Multigrid Quadrature -- Exercises -- References -- Software | |
ISBN: | 9780387215846 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Texts in Applied Mathematics: 43 |
Keywords: | Mathematics , Algebra , Computer mathematics , Numerical analysis , Probabilities , Physics , Computational intelligence , Mathematics , Numerical Analysis , Probability Theory and Stochastic Processes , Algebra , Theoretical, Mathematical and Computational Physics , Computational Intelligence , Computational Mathematics and Numerical Analysis |
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Call number: | SPRINGER-2002-9789401599221:ONLINE Show nearby items on shelf |
Title: | Bounded and Compact Integral Operators |
Author(s): |
David E Edmunds |
Date: | 2002 |
Size: | 1 online resource (643 p.) |
Note: | 10.1007/978-94-015-9922-1 |
Contents: | 1. Hardy-Type Operators -- 2. Fractional Integrals on the Line -- 3. One-Sided Maximal Functions -- 4. Ball Fractional Integrals -- 5. Potentials on RN -- 6. Fractional Integrals on Measure Spaces -- 7. Singular Numbers -- 8. Singular |
Integrals -- 9. Multipliers of Fourier Transforms -- 10. Problems -- References | |
ISBN: | 9789401599221 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 543 |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Integral transforms , Operational calculus , Operator theory , Potential theory (Mathematics) , Mathematics , Potential Theory , Fourier Analysis , Abstract Harmonic Analysis , Integral Transforms, Operational Calculus , Operator Theory |
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Call number: | SPRINGER-2002-9781468492835:ONLINE Show nearby items on shelf |
Title: | Integral Transforms and Their Applications |
Author(s): |
Brian Davies |
Date: | 2002 |
Edition: | Third Edition |
Size: | 1 online resource (370 p.) |
Note: | 10.1007/978-1-4684-9283-5 |
Contents: | 1 Functions of a Complex Variable -- 1.1 Analytic Functions -- 1.2 Contour Integration -- 1.3 Analytic Continuation -- 1.4 Residue Theory -- 1.5 Loop Integrals -- 1.6 Liouville’s Theorem -- 1.7 The Factorial Function -- 1.8 Riemann’s |
Zeta Function -- 2 The Laplace Transform -- 2.1 The Laplace Integral -- 2.2 Important Properties -- 2.3 Simple Applications -- 2.4 Asymptotic Properties: Watson’s Lemma -- Problems -- 3 The Inversion Integral -- 3.1 The | |
Riemann-Lebesgue Lemma -- 3.2 Dirichlet Integrals -- 3.3 The Inversion -- 3.4 Inversion of Rational Functions -- 3.5 Taylor Series Expansion -- 3.6 Inversion of Meromorphic Functions -- 3.7 Inversions Involving a Branch Point -- 3.8 | |
Watson’s Lemma for Loop Integrals -- 3.9 Asymptotic Forms for Large t -- 3.10 Heaviside Series Expansion -- Problems -- 4 Ordinary Differential Equations -- 4.1 Elementary Examples -- 4.2 Higher-Order Equations -- 4.3 Transfer | |
Functions and Block Diagrams -- 4.4 Equations with Polynomial Coefficients -- 4.5 Simultaneous Differential Equations -- 4.6 Linear Control Theory -- 4.7 Realization of Transfer Functions -- Problems -- 5 Partial Differential Equations | |
I -- 5.1 Heat Diffusion: Semi-Infinite Region -- 5.2 Finite Thickness -- 5.3 Wave Propagation -- 5.4 Transmission Line -- Problems -- 6 Integral Equations -- 6.1 Convolution Equations of Volterra Type -- 6.2 Convolution Equations over | |
an Infinite Range -- 6.3 The Percus-Yevick Equation -- Problems -- 7 The Fourier Transform -- 7.1 Exponential, Sine, and Cosine Transforms -- 7.2 Important Properties -- 7.3 Spectral Analysis -- 7.4 Kramers-Krönig Relations -- Problems | |
-- 8 Partial Differential Equations II -- 8.1 Potential Problems -- 8.2 Water Waves: Basic Equations -- 8.3 Waves Generated by a Surface Displacement -- 8.4 Waves Generated by a Periodic Disturbance -- Problems -- 9 Generalized | |
Functions -- 9.1 The Delta Function -- 9.2 Test Functions and Generalized Functions -- 9.3 Elementary Properties -- 9.4 Analytic Functionals -- 9.5 Fourier Transforms of Generalized Functions -- Problems -- 10 Green’s Functions -- 10.1 | |
One-Dimensional Green’s Functions -- 10.2 Green’s Functions as Generalized Functions -- 10.3 Poisson’s Equation in Two Dimensions -- 10.4 Helmholtz’s Equation in Two Dimensions -- Problems -- 11 Transforms in Several Variables -- 11.1 | |
Basic Notation and Results -- 11.2 Diffraction of Scalar Waves -- 11.3 Retarded Potentials of Electromagnetism -- Problems -- 12 The Mellin Transform -- 12.1 Definitions -- 12.2 Simple Examples -- 12.3 Elementary Properties -- 12.4 | |
Potential Problems in Wedge-Shaped Regions -- 12.5 Transforms Involving Polar Coordinates -- 12.6 Hermite Functions -- Problems -- 13 Application to Sums and Integrals -- 13.1 Mellin Summation Formula -- 13.2 A Problem of Ramanujin -- | |
13.3 Asymptotic Behavior of Power Series -- 13.4 Integrals Involving a Parameter -- 13.5 Ascending Expansions for Fourier Integrals -- Problems -- 14 Hankel Transforms -- 14.1 The Hankel Transform Pair -- 14.2 Elementary Properties -- | |
14.3 Some Examples -- 14.4 Boundary-Value Problems -- 14.5 Weber’s Integral -- 14.6 The Electrified Disc -- 14.7 Dual Integral Equations of Titchmarsh Type -- 14.8 Erdelyi-Köber Operators -- Problems -- 15 Integral Transforms Generated | |
by Green’s Functions -- 15.1 The Basic Formula -- 15.2 Finite Intervals -- 15.3 Some Singular Problems -- 15.4 Kontorovich-Lebedev Transform -- 15.5 Boundary-Value Problems in a Wedge -- 15.6 Diffraction of a Pulse by a Two-Dimensional | |
Half-Plane -- Problems -- 16 The Wiener-Hopf Technique -- 16.1 The Sommerfeld Diffraction Problem -- 16.2 Wiener-Hopf Procedure: Half-Plane Problems -- 16.3 Integral and Integro-Differential Equations -- Problems -- 17 Methods Based on | |
Cauchy Integrals -- 17.1 Wiener-Hopf Decomposition by Contour Integration -- 17.2 Cauchy Integrals -- 17.3 The Riemann-Hilbert Problem -- 17.4 Problems in Linear Transport Theory -- 17.5 The Albedo Problem -- 17.6 A Diffraction Problem | |
-- Problems -- 18 Laplace’s Method for Ordinary Differential Equations -- 18.1 Laplace’s Method -- 18.2 Hermite Polynomials -- 18.3 Hermite Functions -- 18.4 Bessel Functions: Integral Representations -- 18.5 Bessel Functions of the | |
First Kind -- 18.6 Functions of the Second and Third Kind -- 18.7 Poisson and Related Representations -- 18.8 Modified Bessel Functions -- Problems -- 19 Numerical Inversion of Laplace Transforms -- 19.1 General Considerations -- 19.2 | |
Gaver-Stehfest Method -- 19.3 Möbius Transformation -- 19.4 Use of Chebyshev Polynomials -- 19.5 Use of Laguerre Polynomials -- 19.6 Representation by Fourier Series -- 19.7 Quotient-Difference Algorithm -- 19.8 Talbot’s Method | |
ISBN: | 9781468492835 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Texts in Applied Mathematics: 41 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Physics , Mathematics , Analysis , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-2002-9781461513155:ONLINE Show nearby items on shelf |
Title: | Applied Mathematics |
Author(s): |
Gerald Dennis Mahan |
Date: | 2002 |
Size: | 1 online resource (368 p.) |
Note: | 10.1007/978-1-4615-1315-5 |
Contents: | 1. Determinants -- 1.1. Cramer’s Rule -- 1.2. Gaussian Elimination -- 1.3. Special Determinants -- 2. Matrices -- 2.1. Several Theorems -- 2.2. Linear Equations -- 2.3. Inverse of a Matrix -- 2.4. Eigenvalues and Eigenvectors -- 2.5. |
Unitary Transformations -- 2.6. Hon-Hermitian Matrices -- 2.7. A Special Matrix -- 2.8. Gram-Schmidt -- 2.9. Chains -- 3. Group Theory -- 3.1. Basic Properties of Groups -- 3.2. Group Representations -- 3.3. Characters -- 3.4. Direct | |
Product Groups -- 3.5. Basis Functions -- 3.6. Angular Momentum -- 3.7. Products of Representations -- 3.8. Quantum Mechanics -- 3.9. Double Groups -- 4. Complex Variables -- 4.1. Introduction -- 4.2. Analytic Functions -- 4.3. | |
Multivalued Functions -- 4.4. Contour Integrals -- 4.5. Meromorphic Functions -- 4.6. Higher Poles -- 4.7. Integrals Involving Branch Cuts -- 4.8. Approximate Evaluation of Integrals -- 5. Series -- 5.1. Taylor Series -- 5.2. | |
Convergence -- 5.3. Laurent Series -- 5.4. Meromorphic Functions -- 5.5. Asymptotic Series -- 5.6. Summing Series -- 5.7. Padé Approximants -- 6. Conformal Mapping -- 6.1. Laplace’s Equation -- 6.2. Mapping -- 6.3. Examples -- 6.4. | |
Schwartz-Christoffel Transformations -- 6.5. van der Pauw -- 7. Markov Averaging -- 7.1. Random Walk -- 7.2. Speckle -- 7.3. Inhomogeneous Broadening -- 8. Fourier Transforms -- 8.1. Fourier Transforms -- 8.2. Laplace Transforms -- | |
8.3. Wavelets -- 9. Equations of Physics -- 9.1. Boundary and Initial Conditions -- 9.2. Boltzmann Equation -- 9.3. Solving Differential Equations -- 9.4. Elliptic Integrals -- 10. One Dimension -- 10.1. Introduction -- 10.2. Diffusion | |
Equation -- 10.3. Wave Equation -- 11. Two Dimensions -- 11.1. Rectangular Coordinates -- 11.2. Polar Coordinates -- 12. Three Dimensions -- 12.1. Cartesian Coordinates -- 12.2. Cylindrical Coordinates -- 12.3. Spherical Coordinates -- | |
12.4. Problems Inside a Sphere -- 12.5. Vector Wave Equation -- 13. Odds and Ends -- 13.1. Hypergeometric Functions -- 13.2. Orthogonal Polynomials -- 13.3. Sturm-Liouville -- 13.4. Green’s Functions -- 13.5. Singular Integral | |
Equations | |
ISBN: | 9781461513155 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Applied mathematics , Engineering mathematics , Physics , Engineering , Materials science , Mathematics , Applications of Mathematics , Theoretical, Mathematical and Computational Physics , Engineering, general , Characterization and Evaluation of Materials |
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Call number: | SPRINGER-2002-9781461507772:ONLINE Show nearby items on shelf |
Title: | Nonlinear Problems in Mathematical Physics and Related Topics I In Honor of Professor O. A. Ladyzhenskaya |
Author(s): | |
Date: | 2002 |
Size: | 1 online resource (386 p.) |
Note: | 10.1007/978-1-4615-0777-2 |
Contents: | Area Formulas for ?-Harmonic Mappings -- On a Variational Problem Connected with Phase Transitions of Means in Controllable Dynamical Systems -- A Priori Estimates for Starshaped Compact Hypersurfaces with Prescribed mth Curvature |
Function in Space Forms -- Elliptic Variational Problems with Nonstandard Growth -- Existence and Regularity of Solutions of d? = f with Dirichlet Boundary Conditions. -- A Singular Perturbation Property of Capillary Surfaces -- On | |
Solutions with Fast Decay of Nonstationary Navier-Stokes System in the Half-Space -- Strong Solutions to the Problem of Motion of a Rigid Body in a Navier-Stokes Liquid under the Action of Prescribed Forces and Torques -- The Partially | |
Free Boundary Problem for Parametric Double Integrals -- On Evolution Laws Forcing Convex Surfaces to Shrink to a Point -- Existence of a Generalized Green Function for Integro-Differential Operators of Fractional Order -- Lq-Estimates | |
of the First-Order Derivatives of Solutions to the Nonstationary Stokes Problem -- Two Sufficient Conditions for the Regularity of Lateral Boundary for the Heat Equation -- Bound State Asymptotics for Elliptic Operators with Strongly | |
Degenerated Symbols -- Nonlocal Problems for Quasilinear Parabolic Equations -- Boundary Feedback Stabilization of a Vibrating String with an Interior Point Mass -- On Direct Lyapunov Method in Continuum Theories -- The Fourier | |
Coefficients of Stokes’ Waves -- A Geometric Regularity Estimate via Fully Nonlinear Elliptic Equations -- On the Eigenvalue Estimates for the Weighted Laplacian on Metric Graphs -- Potential Theory for Nonstationary Stokes Problem in | |
Nonconvex Domains -- Stability of Axially Symmetric Solutions to the Navier-Stokes Equations in Cylindrical Domains | |
ISBN: | 9781461507772 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | International Mathematical Series: 1 |
Keywords: | Mathematics , Partial differential equations , Applied mathematics , Engineering mathematics , Continuum physics , Fluids , Mathematics , Partial Differential Equations , Fluid- and Aerodynamics , Mathematics, general , Classical Continuum Physics , Applications of Mathematics |
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Call number: | SPRINGER-2002-9781461201014:ONLINE Show nearby items on shelf |
Title: | Computational Methods for Linear Integral Equations |
Author(s): |
Prem K Kythe |
Date: | 2002 |
Size: | 1 online resource (508 p.) |
Note: | 10.1007/978-1-4612-0101-4 |
Contents: | 1 Introduction -- 1 1 Notation and Definitions -- 1.2 Classification -- 1.3 Function Spaces -- 1.4 Convergence -- 1.5 Inverse Operator -- 1.6 Nyström System -- 1.7 Other Types of Kernels -- 1.8 Neumann Series -- 1.9 Resolvent Operator |
-- 1.10 Fredholm Alternative -- 2 Eigenvalue Problems -- 2.1 Linear Symmetric Equations -- 2.2 Residual Methods -- 2.3 Degenerate Kernels -- 2.4 Replacement by a Degenerate Kernel -- 2.5 Baterman’s Method -- 2.6 Generallized Eigenvalue | |
Problem -- 2.7 Applications -- 3 Equations of the Second Kind -- 3.1 Fredholm Equations -- 3.2 Volterra Equations -- 4 Classical Methods for FK2 -- 4.1 Expansion Method -- 4.2 Product-Integration Method -- 4.3 Quadrature Method -- 4.4 | |
Deferred Correction Methods -- 4.5 A Modified Quadrature Method -- 4.6 Collocation Methods -- 4.7 Elliott’s Modification -- 5 Variational Methods -- 5.1 Galerkin Method -- 5.2 Ritz-Galerkin Methods -- 5.3 Special Cases -- 5.4 | |
Fredholm-Nyström System -- 6 Iteration Methods -- 6.1 Simple Iterations -- 6.2 Quadrature Formulas -- 6.3 Error Analysis -- 6.4 Iterative Scheme -- 6.5 Krylov-Bogoliubov Method -- 7 Singular Equations -- 7.1 Singularities in Linear | |
Equations -- 7.2 Fredholm Theorems -- 7.3 Modified Quadrature Rule -- 7.4 Convolution-Type Kernels -- 7.5 Volterra-Type Singular Equations -- 7.6 Convolution Methods -- 7.7 Asymptotic Methods for Log-Singular Equations -- 7.8 Iteration | |
Methods -- 7.9 Singular Equations with the Hilbert Kernel -- 7.10 Finite-Part Singular Equations -- 8 Weakly Singular Equations -- 8.1 Weakly Singular Kernel -- 8.2 Taylor’s Series Method -- 8.3 Lp-Approximation Method -- 8.4 | |
Product-Integration Method -- 8.5 Splines Method -- 8.6 Weakly Singular Volterra Equations -- 9 Cauchy Singular Equations -- 9.1 Cauchy Singular Equations of the First Kind -- 9.2 Approximation by Trigonometric Polynomials -- 9.3 | |
Cauchy Singular Equations of the Second Kind -- 9.4 From CSK2 to FK2 -- 9.5 Gauss-Jacobi Quadrature -- 9.6 Collocation Method for CSK1 -- 10 Sinc-Galerkin Methods -- 10.1 Sine Function Approximations -- 10.2 Conformal Maps and | |
Interpolation -- 10.3 Approximation Theory -- 10.4 Convergence -- 10.5 Sinc-Galerkin Scheme -- 10.6 Computation Guidelines -- 10.7 Sine-Collocation Method -- 10.8 Single-Layer Potential -- 10.9 Double-Layer Problem -- 11 Equations of | |
the First Kind -- 11.1 Inherent Ill-Posedness -- 11.2 Separable Kernels -- 11.3 Some Theorems -- 11.4 Numerical Methods -- 11.5 Volterra Equations of the First Kind -- 11.6 Abel’s Equation -- 11.7 Iterative Schemes -- 12 Inversion of | |
Laplace Transforms -- 12.1 Laplace Transforms -- 12.2 General Interpolating Scheme -- 12.3 Inversion by Fourier Series -- 12.4 Inversion by the Riemann Sum -- 12.5 Approximate Formulas -- A Quadrature Rules -- A. 1 Newton-Cotes | |
Quadratures -- A.2 Gaussian Quadratures -- A.3 Integration of Products -- A.4 Singular Integrals -- A.5 Infinite-Range Integrals -- A. 6 Linear Transformation of Quadratures -- A.7 Trigonometric Polynomials -- A.8 Condition Number -- | |
A.7 Quadrature Tables -- B Orthogonal Polynomials -- B.l Zeros of Some Orthogonal Polynomials -- C Whittaker’s Cardinal Function -- C. 1 Basic Results -- C.2 Approximation of an Integral -- D Singular Integrals -- D.l Cauchy’s | |
Principal-Value Integrals -- D.2 P.V. of a Singular Integral on a Contour -- D.3 Hadamard’s Finite-Part Integrals -- D.4 Two-Sided Finite-Part Integrals -- D.5 One-Sided Finite-Part Integrals -- D.6 Examples of Cauchy P.V. Integrals -- | |
D.7 Examples of Hadamard’s Finite-Part Integrals | |
ISBN: | 9781461201014 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Numerical analysis , Integral equations , Functions of complex variables , Mathematics , Integral Equations , Numeric Computing , Several Complex Variables and Analytic Spaces |
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Call number: | SPRINGER-2001-9789401597975:ONLINE Show nearby items on shelf |
Title: | Asymptotics of Linear Differential Equations |
Author(s): |
M. H Lantsman |
Date: | 2001 |
Size: | 1 online resource (441 p.) |
Note: | 10.1007/978-94-015-9797-5 |
Contents: | 1. Introduction -- 2. Metric spaces -- 3. Asymptotic spaces -- 4. Asymptotic behaviour of functions -- 5. Power order growth functions on the positive semi-axis -- 6. Power order growth functions of the complex argument -- 7. |
Integrals -- 8. Linear differential equations -- 9. General asymptotic properties of linear differential equations -- 10. Linear differential equations with power order growth coefficients on the positive semi-axis -- 11. Linear | |
differential equations in singular cases on the positive semi-axis -- 12. Linear differential equations in a sector of the complex plane -- 13. Linear differential equations with power-logarithmic coefficients -- 14. Linear difference | |
equations. General theory -- 15. Asymptotic behaviour of solutions of linear difference equations -- 16. Supplement -- List of symbols | |
ISBN: | 9789401597975 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 533 |
Keywords: | Mathematics , Harmonic analysis , Difference equations , Functional equations , Operator theory , Differential equations , Sequences (Mathematics) , Mathematics , Ordinary Differential Equations , Difference and Functional Equations , Operator Theory , Abstract Harmonic Analysis , Sequences, Series, Summability |
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Call number: | SPRINGER-2001-9783642566660:ONLINE Show nearby items on shelf |
Title: | Computer Algebra in Scientific Computing CASC 2001 Proceedings of the Fourth International Workshop on Computer Algebra in Scientific Computing, Konstanz, Sept. 22-26, 2001 |
Author(s): | |
Date: | 2001 |
Size: | 1 online resource (555 p.) |
Note: | 10.1007/978-3-642-56666-0 |
Contents: | Jets. A Maple-Package for Formal Differential Geometry -- Computing Stratifications of Quotients of Finite Groups and an Application to Shape Memory Alloy -- A MuPAD Library for Differential Equation -- Algebraic Identification |
Algorithm and Application to Dynamical Systems -- Cooperation Between a Dynamic Geometry Environment and a Computer Algebra System for Geometric Discovery -- On the Stability of Steady Motions of a Solar-Sail Satellite -- Application | |
of Computer Algebra for Investigation of a Group Properties of the Navier-Stokes Equations for Compressible Viscous Heat-Conducting Gas -- Mathematica and Nilpotent Lie Superalgebras -- Neighborhoods of an Ordinary Linear Differential | |
Equation -- Invariants of Finite Groups and Involutive Division -- Symbolic Computation and Boundary Conditions for the Wave Equation -- Parametric Systems of Linear Congruences -- Bifurcation Analysis of Low Resonant Case of the | |
Generalized Henon - Heiles System -- An Involutive Reduction Method to Find Invariant Solutions for Partial Differential Equations -- Recurrence Functions and Numerical Characteristics of Graphs -- A New Combinatorial Algorithm for | |
Large Markov Chains -- GROOME - Tool Supported Graphical Object Oriented Modelling for Computer Algebra and Scientific Computing -- Construction of Janet Bases I.Monomial Bases -- Construction of Janet Bases II.Polynomial Bases -- | |
Low-Dimensional Quasi-Filiform Lie Algebras with Great Length -- Algebraic Methods for Sectioning Parametric Surfaces -- The Methods of Computer Algebra and the Arnold-Moser Theorem -- Symbolic Algorithms of Algebraic Perturbation | |
Theory: Hydrogen Atom in the Field of Distant Charge -- Perturbation versus Differentiation Indices -- Employment of the Gröbner Bases in Analysis of Systems Having Algebraic First Integrals -- “Coalgebra” Structures on 1-Homological | |
Models for Commutative Differential Graded Algebras -- Conservative Finite Difference Schemes for Cosymmetric Systems -- A Mathematica Solver for Two-Point Singularly-Perturbed Boundary Value Problems -- A New Algorithm for Computing | |
Cohomologies of Lie Superalgebras -- Parallel Computing with Mathematica -- Solution of Systems of Linear Diophantine Equations -- SYMOPT: Symbolic Parametric Mathematical Programming -- Representing Graph Properties by Polynomial | |
Ideals -- Parametric G1-Blending of Several Surfaces -- A Method of Logic Deduction and Verification in KBS Using Positive Integers -- Progressive Long Waves on a Slope (A New Solution to the Euler Equation?) -- The Method of Newton | |
Polyhedra for Investigating Singular Positions of Some Mechanisms -- Algebraic Predicates for Empirical Data -- Fractional Driftless Fokker-Planck Equation with Power Law Diffusion Coefficients -- Factorization of Overdetermined | |
Systems of Linear Partial Differential Equations with Finite-Dimensional Solution Space -- Semilinear Motion Planning Among Moving Objects in REDLOG -- Author Index | |
ISBN: | 9783642566660 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algorithms , Physics , Mathematics , Algorithms , Theoretical, Mathematical and Computational Physics , Algorithm Analysis and Problem Complexity |
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Call number: | SPRINGER-2001-9781461221005:ONLINE Show nearby items on shelf |
Title: | Dimensionality Reducing Expansion of Multivariate Integration |
Author(s): |
Tian-Xiao He |
Date: | 2001 |
Size: | 1 online resource (227 p.) |
Note: | 10.1007/978-1-4612-2100-5 |
Contents: | 1 Dimensionality Reducing Expansion of Multivariate Integration -- 1.1 Darboux formulas and their special forms -- 1.2 Generalized integration by parts rule -- 1.3 DREs with algebraic precision -- 1.4 Minimum estimation of remainders |
in DREs with algebraic precision -- 2 Boundary Type Quadrature Formulas with Algebraic Precision -- 2.1 Construction of BTQFs using DREs -- 2.2 BTQFs with homogeneous precision -- 2.3 Numerical integration associated with wavelet | |
functions -- 2.4 Some applications of DREs and BTQFs -- 2.5 BTQFs over axially symmetric regions -- 3 The Integration and DREs of Rapidly Oscillating Functions -- 3.1 DREs for approximating a double integral -- 3.2 Basic lemma -- 3.3 | |
DREs with large parameters -- 3.4 Basic expansion theorem for integrals with large parameters -- 3.5 Asymptotic expansion formulas for oscillatory integrals with singular factors -- 4 Numerical Quadrature Formulas Associated with the | |
Integration of Rapidly Oscillating Functions -- 4.1 Numerical quadrature formulas of double integrals -- 4.2 Numerical integration of oscillatory integrals -- 4.3 Numerical quadrature of strongly oscillatory integrals with compound | |
precision -- 4.4 Fast numerical computations of oscillatory integrals -- 4.5 DRE construction and numerical integration using measure theory -- 4.6 Error analysis of numerical integration -- 5 DREs Over Complex Domains -- 5.1 DREs of | |
the double integrals of analytic functions -- 5.2 Construction of quadrature formulas using DREs -- 5.3 Integral regions suitable for DREs -- 5.4 Additional topics -- 6 Exact DREs Associated With Differential Equations -- 6.1 DREs and | |
ordinary differential equations -- 6.2 DREs and partial differential equations -- 6.3 Applications of DREs in the construction of BTQFs -- 6.4 Applications of DREs in the boundary element method | |
ISBN: | 9781461221005 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Partial differential equations , Applied mathematics , Engineering mathematics , Computer mathematics , Numerical analysis , Statistics , Mathematics , Numerical Analysis , Computational Mathematics and Numerical Analysis , Partial Differential Equations , Applications of Mathematics , Statistics for Business/Economics/Mathematical Finance/Insurance |
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Call number: | SPRINGER-2000-9783642571497:ONLINE Show nearby items on shelf |
Title: | Introduction to Calculus and Analysis II/1 |
Author(s): |
Richard Courant |
Date: | 2000 |
Size: | 1 online resource (556 p.) |
Note: | 10.1007/978-3-642-57149-7 |
Contents: | 1 Functions of Several Variables and Their Derivatives -- 1.1 Points and Points Sets in the Plane and in Space -- 1.2 Functions of Several Independent Variables -- 1.3 Continuity -- 1.4 The Partial Derivatives of a Function -- 1.5 The |
Differential of a Function and Its Geometrical Meaning -- 1.6 Functions of Functions (Compound Functions) and the Introduction of New In-dependent Variables -- 1.7 The Mean Value Theorem and Taylor’s Theorem for Functions of Several | |
Variables -- 1.8 Integrals of a Function Depending on a Parameter -- 1.9 Differentials and Line Integrals -- 1.10 The Fundamental Theorem on Integrability of Linear Differential Forms -- Appendix A.1. The Principle of the Point of | |
Accumulation in Several Dimensions and Its Applications -- A.2. Basic Properties of Continuous Functions -- A.3. Basic Notions of the Theory of Point Sets -- A.4. Homogeneous functions. -- 2 Vectors, Matrices, Linear Transformations -- | |
2.1 Operations with Vectors -- 2.2 Matrices and Linear Transformations -- 2.3 Determinants -- 2.4 Geometrical Interpretation of Determinants -- 2.5 Vector Notions in Analysis -- 3 Developments and Applications of the Differential | |
Calculus -- 3.1 Implicit Functions -- 3.2 Curves and Surfaces in Implicit Form -- 3.3 Systems of Functions, Transformations, and Mappings -- 3.4 Applications -- 3.5 Families of Curves, Families of Surfaces, and Their Envelopes -- 3.6 | |
Alternating Differential Forms -- 3.7 Maxima and Minima -- Appendix A.1 Sufficient Conditions for Extreme Values -- A.2 Numbers of Critical Points Related to Indices of a Vector Field -- A.3 Singular Points of Plane Curves 360 A.4 | |
Singular Points of Surfaces -- A.5 Connection Between Euler’s and Lagrange’s Representation of the motion of a Fluid -- A.6 Tangential Representation of a Closed Curve and the Isoperi-metric Inequality -- 4 Multiple Integrals -- 4.1 | |
Areas in the Plane -- 4.2 Double Integrals -- 4.3 Integrals over Regions in three and more Dimensions -- 4.4 Space Differentiation. Mass and Density -- 4.5 Reduction of the Multiple Integral to Repeated Single Integrals -- 4.6 | |
Transformation of Multiple Integrals -- 4.7 Improper Multiple Integrals -- 4.8 Geometrical Applications -- 4.9 Physical Applications -- 4.10 Multiple Integrals in Curvilinear Coordinates -- 4.11 Volumes and Surface Areas in Any Number | |
of Dimensions -- 4.12 Improper Single Integrals as Functions of a Parameter -- 4.13 The Fourier Integral -- 4.14 The Eulerian Integrals (Gamma Function) -- Appendix: Detailed Analysis of the Process Of Integration A.1 Area -- A.2 | |
Integrals of Functions of Several Variables -- A.3 Transformation of Areas and Integrals -- A.4 Note on the Definition of the Area of a Curved Surface -- 5 Relations Between Surface and Volume Integrals -- 5.1 Connection Between Line | |
Integrals and Double Integrals in the Plane (The Integral Theorems of Gauss, Stokes, and Green) -- 5.2 Vector Form of the Divergence Theorem. Stokes’s Theorem -- 5.3 Formula for Integration by Parts in Two Dimensions. Green’s Theorem | |
-- 5.4 The Divergence Theorem Applied to the Transformation of Double Integrals -- 5.5 Area Differentiation. Transformation of Au to Polar Coordinates -- 5.6 Interpretation of the Formulae of Gauss and Stokes by Two-Dimensional Flows | |
-- 5.7 Orientation of Surfaces -- 5.8 Integrals of Differential Forms and of Scalars over Surfaces -- 5.9 Gauss’s and Green’s Theorems in Space -- 5.10 Stokes’s Theorem in Space -- 5.11 Integral Identities in Higher Dimensions -- | |
Appendix: General Theory Of Surfaces And Of Surface Integals A.I Surfaces and Surface Integrals in Three dimensions -- A.2 The Divergence Theorem -- A.3 Stokes’s Theorem -- A.4 Surfaces and Surface Integrals in Euclidean Spaces of | |
Higher Dimensions -- A.5 Integrals over Simple Surfaces, Gauss’s Divergence Theorem, and the General Stokes Formula in Higher Dimensions -- 6 Differential Equations -- 6.1 The Differential Equations for the Motion of a Particle in | |
Three Dimensions -- 6.2 The General Linear Differential Equation of the First Order -- 6.3 Linear Differential Equations of Higher Order -- 6.4 General Differential Equations of the First Order -- 6.5 Systems of Differential Equations | |
and Differential Equations of Higher Order -- 6.6 Integration by the Method of Undermined Coefficients -- 6.7 The Potential of Attracting Charges and Laplace’s Equation -- 6.8 Further Examples of Partial Differential Equations from | |
Mathematical Physics -- 7 Calculus of Variations -- 7.1 Functions and Their Extrema -- 7.2 Necessary conditions for Extreme Values of a Functional -- 7.3 Generalizations -- 7.4 Problems Involving Subsidiary Conditions. Lagrange | |
Multipliers -- 8 Functions of a Complex Variable -- 8.1 Complex Functions Represented by Power Series -- 8.2 Foundations of the General Theory of Functions of a Complex Variable -- 8.3 The Integration of Analytic Functions -- 8.4 | |
Cauchy’s Formula and Its Applications -- 8.5 Applications to Complex Integration (Contour Integration) -- 8.6 Many-Valued Functions and Analytic Extension -- List of Biographical Dates | |
ISBN: | 9783642571497 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis |
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Call number: | SPRINGER-2000-9783642571343:ONLINE Show nearby items on shelf |
Title: | Bifurcations and Catastrophes Geometry of Solutions to Nonlinear Problems |
Author(s): |
Michel Demazure |
Date: | 2000 |
Size: | 1 online resource (304 p.) |
Note: | 10.1007/978-3-642-57134-3 |
Contents: | 1. Local Inversion -- 1.1 Introduction -- 1.2 A Preliminary Statement -- 1.3 Partial Derivatives. Strictly Differentiable Functions -- 1.4 The Local Inversion Theorem: General Statement -- 1.5 Functions of Class Cr -- 1.6 The Local |
Inversion Theorem for Crmaps -- 1.7 Curvilinear Coordinates -- 1.8 Generalizations of the Local Inversion Theorem -- 2. Submanifolds -- 2.1 Introduction -- 2.2 Definitions of Submanifolds -- 2.3 First Examples -- 2.4 Tangent Spaces of | |
a Submanifold -- 2.5 Transversality: Intersections -- 2.6 Transversality: Inverse Images -- 2.7 The Implicit Function Theorem -- 2.8 Diffeomorphisms of Submanifolds -- 2.9 Parametrizations, Immersions and Embeddings -- 2.10 Proper Maps | |
Proper Embeddings -- 2.11 From Submanifolds to Manifolds -- 2.12 Some History -- 3. Transversality Theorems -- 3.1 Introduction -- 3.2 Countability Properties in Topology -- 3.3 Negligible Subsets -- 3.4 The Complement of the Image of | |
a Submanifold -- 3.5 Sard’s Theorem -- 3.6 Critical Points, Submersions and the Geometrical Form of Sard’s Theorem -- 3.7 The Transversality Theorem: Weak Form -- 3.8 Jet Spaces -- 3.9 The Thorn Transversality Theorem -- 3.10 Some | |
History -- 4. Classification of Differentiable Functions -- 4.1 Introduction -- 4.2 Taylor Formulae Without Remainder -- 4.3 The Problem of Classification of Maps -- 4.4 Critical Points: the Hessian Form -- 4.5 The Morse Lemma -- 4.6 | |
Bifurcations of Critical Points -- 4.7 Apparent Contour of a Surface in R3 -- 4.8 Maps from R2 into R2 -- 4.9 Envelopes of Plane Curves -- 4.10 Caustics -- 4.11 Genericity and Stability -- 5. Catastrophe Theory -- 5.1 Introduction -- | |
5.2 The Language of Germs -- 5.3 r-sufficient Jets r-determined Germs -- 5.4 The Jacobian Ideal -- 5.5 The Theorem on Sufficiency of Jets -- 5.6 Deformations of a Singularity -- 5.7 The Principles of Catastrophe Theory -- 5.8 | |
Catastrophes of Cusp Type -- 5.9 A Cusp Example -- 5.10 Liquid-Vapour Equilibrium -- 5.11 The Elementary Catastrophes -- 5.12 Catastrophes and Controversies -- 6. Vector Fields -- 6.1 Introduction -- 6.2 Examples of Vector Fields (Rn | |
Case) -- 6.3 First Integrals -- 6.4 Vector Fields on Submanifolds -- 6.5 The Uniqueness Theorem and Maximal Integral Curves -- 6.6 Vector Fields and Line Fields. Elimination of the Time -- 6.7 One-parameter Groups of Diffeomorphisms -- | |
6.8 The Existence Theorem (Local Case) -- 6.9 The Existence Theorem (Global Case) -- 6.10 The Integral Flow of a Vector Field -- 6.11 The Main Features of a Phase Portrait -- 6.12 Discrete Flows and Continuous Flows -- 7. Linear Vector | |
Fields -- 7.1 Introduction -- 7.2 The Spectrum of an Endomorphism -- 7.3 Space Decomposition Corresponding to Partition of the Spectrum -- 7.4 Norm and Eigenvalues -- 7.5 Contracting, Expanding and Hyperbolic Endomorphisms -- 7.6 The | |
Exponential of an Endomorphism -- 7.7 One-parameter Groups of Linear Transformations -- 7.8 The Image of the Exponential -- 7.9 Contracting, Expanding and Hyperbolic Exponential Flows -- 7.10 Topological Classification of Linear Vector | |
Fields -- 7.11 Topological Classification of Automorphisms -- 7.12 Classification of Linear Flows in Dimension 2 -- 8. Singular Points of Vector Fields -- 8.1 Introduction -- 8.2 The Classification Problem -- 8.3 Linearization of a | |
Vector Field in the Neighbourhood of a Singular Point -- 8.4 Difficulties with Linearization -- 8.5 Singularities with Attracting Linearization -- 8.6 Lyapunov Theory -- 8.7 The Theorems of Grobman and Hartman -- 8.8 Stable and | |
Unstable Manifolds of a Hyperbolic Singularity -- 8.9 Differentable Linearization: Statement of the Problem -- 8.10 Differentiable Linearization: Resonances -- 8.11 Differentiable Linearization: the Theorems of Sternberg and Hartman -- | |
8.12 Linearization in Dimension 2 -- 8.13 Some Historical Landmarks -- 9. Closed Orbits—Structural Stability -- 9.1 Introduction -- 9.2 The Poincaré Map -- 9.3 Characteristic Multipliers of a Closed Orbit -- 9.4 Attracting Closed | |
Orbits -- 9.5 Classification of Closed Orbits and Classification of Diffeomorphisms -- 9.6 Hyperbolic Closed Orbits -- 9.7 Local Structural Stability -- 9.8 The Kupka-Smale Theorem -- 9.9 Morse-Smale Fields -- 9.10 Structural Stability | |
Through the Ages -- 10.Bifurcations of Phase Portraits -- 10.1 Introduction -- 10.2 What Do We Mean by Bifurcation? -- 10.3 The Centre Manifold Theorem -- 10.4 The Saddle-Node Bifurcation -- 10.5 The Hopf Bifurcation -- 10.6 Local | |
Bifurcations of a Closed Orbit -- 10.7 Saddle-node Bifurcation for a Closed Orbit -- 10.8 Period-doubling Bifurcation -- 10.9 Hopf Bifurcation for a Closed Orbit -- 10.10 An Example of a Codimension 2 Bifurcation -- 10.11 An Example of | |
Non-local Bifurcation -- References -- Notation | |
ISBN: | 9783642571343 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Dynamics , Ergodic theory , Global analysis (Mathematics) , Manifolds (Mathematics) , Differential geometry , Mathematics , Differential Geometry , Global Analysis and Analysis on Manifolds , Dynamical Systems and Ergodic Theory |
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Call number: | SPRINGER-2000-9783034883832:ONLINE Show nearby items on shelf |
Title: | Stochastic Processes in Quantum Physics |
Author(s): |
Masao Nagasawa |
Date: | 2000 |
Size: | 1 online resource (598 p.) |
Note: | 10.1007/978-3-0348-8383-2 |
Contents: | I Markov Processes -- 1.1 Classical Mechanics -- 1.2 Movement of a Particle with Noise -- 1.3 Transition Probability and the Markov Property -- 1.4 Diffusion Equations -- 1.5 Brownian Motions -- 1.6 The Itô formula -- Appendix. |
Monotone Lemmas -- II Time Reversal and Duality -- 2.1 Time Reversal of Markov Processes and Duality -- 2.2 Space-Time Markov Processes and Space-Time Duality -- 2.3 Time Reversal and Schrödinger’s Representation -- III | |
Non-Relativistic Quantum Theory -- 3.1 Non-Relativistic Equation of Motion -- 3.2 Stationary States and Eigenvalue Problem -- 3.3 Time Reversal of Diffusion Processes -- 3.4 Duality Relation of Diffusion Processes -- 3.5 Equation of | |
Motion in General Cases -- 3.6 Principle of Superposition of Markov Processes -- 3.7 Non-Relativistic Schrödinger Equation -- 3.8 State Preparations and Measurements -- 3.9 Diffusion or Schrödinger Equations ? -- 3.10 The First | |
Technical Convention -- IV Stationary Schrödinger Processes -- 4.1 Stationary States -- 4.2 One-Dimensional Harmonic Oscillator -- 4.3 An Example in Two-Dimension -- 4.4 Superposition of Eigenfunctions -- 4.5 Further Excited States -- | |
4.6 Hydrogen Atom -- V Construction of the Schrödinger Processes -- 5.1 The Feynman-Kac Formula -- 5.2 Solving the Equation of Motion -- 5.3 Transformation by Multiplicative Functionals -- 5.4 Renormalization -- 5.5 A Variational | |
Method -- 5.6 The Maruyama-Girsanov Formula -- 5.7 A Lagrangian Formulation -- 5.8 The Second Technical Convention -- VI Markov Processes with Jumps -- 6.1 Poisson and Compound Poisson Processes -- 6.2 Poisson Random measures and Point | |
Processes -- 6.3 Stochastic Integrals with Poisson Point Processes -- 6.4 Lévy Processes -- 6.5 Stable Processes -- 6.6 Bochner’s Subordination -- 6.7 Duality of Subordinate Semi-Groups -- 6.8 Harmonic Transformation of Subordinate | |
Semi-Groups -- 6.9 Duality of Fractional Powers of Time-Dependent Operators -- VII Relativistic Quantum Particles -- 7.1 A Relativistic Schrödinger Equation for a Spinless Paticle -- 7.2 Equation of Motion for Relativistic Quantum | |
Particles -- 7.3 Stationary States of the Relativistic Schrödinger Equation -- 7.4 Stochastic Processes for Relativistic Spinless Particles -- 7.5 Non-Relativistic Limit -- 7.6 A Diffusion Approximation -- VIII Stochastic Differential | |
Equations of Pure-Jumps -- 8.1 Markov Processes with the Generators of Fractional Power -- 8.2 Stochastic Differential Equations of Pure-Jumps -- 8.3 The Case with no Potential Term -- 8.4 To Solve the Stochastic Differential Equations | |
of Pure-Jumps -- 8.5 To Construct Pure-Jump Markov Processes -- 8.6 A Remark on the Integrability Condition -- IX Variational Principle for Relativistic Quantum Particles -- 9.1 Absolute Continuity -- 9.2 Pure-Jump Markov Processes -- | |
9.3 A Multiplicative Functional -- 9.4 Renormalization and Variational Principle -- X Time Dependent Subordination and Markov Processes with Jumps -- 10.1 Time-Inhomogeneous Subordination -- 10.2 Lemmas -- 10.3 Stochastic Differential | |
Equation with Jumps -- 10.4 A Formula of Feynman-Kac Type -- 10.5 Markov Processes with Jumps -- Appendix. Integration by Parts Formulae -- XI Concave Majorants of Lévy Processes and the Light Cone -- 14.1 The Vertex Process of a Lévy | |
Process -- 14.2 Propositions on Random walks -- 14.3 Proof of Propositions on Random Walks -- 14.4 Proof of the main Theorems -- 14.5 Examples -- 14.6 The light Cone -- XII The Locality in Quantum Physics -- 12.1 Historical Overview -- | |
12.2 Hidden-Variable Theories -- 12.3 Locality of Hidden-Variable Theories -- 12.4 Spin-Correlation of Three Particles -- 12.5 Gudder’s Hidden-Variable Theory -- 12.6 Spin-Correlations in Gudder’s Theory -- 12.7 Some Remarks -- XIII | |
Micro Statistical Theory -- 13.1 The Source of the Noise -- 13.2 Large Deviations of the Renormalized Processes -- 13.3 The Propagation of Chaos -- 13.4 Micro Statistical Mechanics -- 13.5 Propagation of Chaos of Pure-Jump Processes -- | |
13.6 Superposition of Movements -- 12.7 A Remark on the Gibbs Distribution -- XIV Processes on Open Time Intervals -- 14.1 Diffusion Processes on Open Time Intervals -- 14.2 Time-Reversed Schrödinger Processes -- 14.3 A Theorem of | |
Jeulin-Yor -- 14.4 Reflecting Brownian Motion -- 14.5 Two-Sided Skorokhod Type Problem -- 14.6 Skorokhod Problem with Singular Drift -- 14.7 The Minimum and Maximum Solutions -- 14.8 The Uniqueness and Non-Uniqueness of Solutions -- | |
14.9 An Application: The Origin of Universes -- XV Creation and Killing of Particles -- 15.1 Non-Linear Differential Equations -- 15.2 Branching Markov Processes -- 15.3 The Expected Number of Particles -- 15.4 Killing -- XVI The ltô | |
Calculus -- 16.1 The Itô Integral -- 16.2 Martingales -- 16.3 The Itô Integral with Local Martingales -- 16.4 Itô’s formula -- 16.5 Stochastic Differential Equations -- 16.6 Stochastic Differential Calculus -- References | |
ISBN: | 9783034883832 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Monographs in Mathematics : 94 |
Keywords: | Mathematics , Probabilities , Quantum physics , Mathematics , Probability Theory and Stochastic Processes , Quantum Physics |
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Call number: | SPRINGER-2000-9781461213826:ONLINE Show nearby items on shelf |
Title: | Singular Integral Equations |
Author(s): |
Ricardo Estrada |
Date: | 2000 |
Size: | 1 online resource (427 p.) |
Note: | 10.1007/978-1-4612-1382-6 |
Contents: | 1 Reference Material -- 1.1 Introduction -- 1.2 Singular Integral Equations -- 1.3 Improper Integrals -- 1.4 The Lebesgue Integral -- 1.5 Cauchy Principal Value for Integrals -- 1.6 The Hadamard Finite Part -- 1.7 Spaces of Functions |
and Distributions -- 1.8 Integral Transform Methods -- 1.9 Bibliographical Notes -- 2 Abel’s and Related Integral Equations -- 2.1 Introduction -- 2.2 Abel’s Equation -- 2.3 Related Integral Equations -- 2.4 The equation $$\int_{0}^{s} | |
{{{{(s - t)}}^{\beta }}g(t)dt = f(s), \Re e \beta > - 1}$$ -- 2.5 Path of Integration in the Complex Plane -- 2.6 The Equation $$\int_{{{{C}_{{a\xi }}}}} {\frac{{g(z)dz}}{{{{{(z - \xi )}}^{\nu }}}}} + k\int_{{{{C}_{{\xi b}}}}} | |
{\frac{{g(z)dz}}{{{{{(\xi - z)}}^{\nu }}}}} = f(\xi )$$ -- 2.7 Equations on a Closed Curve -- 2.8 Examples -- 2.9 Bibliographical Notes -- 2.10 Problems -- 3 Cauchy Type Integral Equations -- 3.1 Introduction -- 3.2 Cauchy Type | |
Equation of the First Kind -- 3.3 An Alternative Approach -- 3.4 Cauchy Type Equations of the Second Kind -- 3.5 Cauchy Type Equations on a Closed Contour -- 3.6 Analytic Representation of Functions -- 3.7 Sectionally Analytic | |
Functions (z?a)n?v(z?b)m+v -- 3.8 Cauchy’s Integral Equation on an Open Contour -- 3.9 Disjoint Contours -- 3.10 Contours That Extend to Infinity -- 3.11 The Hilbert Kernel -- 3.12 The Hilbert Equation -- 3.13 Bibliographical Notes -- | |
3.14 Problems -- 4 Carleman Type Integral Equations -- 4.1 Introduction -- 4.2 Carleman Type Equation over a Real Interval -- 4.3 The Riemann-Hilbert Problem -- 4.4 Carleman Type Equations on a Closed Contour -- 4.5 Non-Normal Problems | |
-- 4.6 A Factorization Procedure -- 4.7 An Operational Approach -- 4.8 Solution of a Related Integral Equation -- 4.9 Bibliographical Notes -- 4.10 Problems -- 5 Distributional Solutions of Singular Integral Equations -- 5.1 | |
Introduction -- 5.2 Spaces of Generalized Functions -- 5.3 Generalized Solution of the Abel Equation -- 5.4 Integral Equations Related to Abel’s Equation -- 5.5 The Fractional Integration Operators ?? -- 5.6 The Cauchy Integral | |
Equation over a Finite Interval -- 5.7 Analytic Representation of Distributions of ?’[a, b] -- 5.8 Boundary Problems in A[a,b] -- 5.9 Disjoint Intervals -- 5.10 Equations Involving Periodic Distributions -- 5.11 Bibliographical Notes | |
-- 5.12 Problems -- 6 Distributional Equations on the Whole Line -- 6.1 Introduction -- 6.2 Preliminaries -- 6.3 The Hilbert Transform of Distributions -- 6.4 Analytic Representation -- 6.5 Asymptotic Estimates -- 6.6 Distributional | |
Solutions of Integral Equations -- 6.7 Non-Normal Equations -- 6.8 Bibliographical Notes -- 6.9 Problems -- 7 Integral Equations with Logarithmic Kernels -- 7.1 Introduction -- 7.2 Expansion of the Kernel In |x-y| -- 7.3 The Equation | |
$$\int_{a}^{b} {\ln } \left| {x - y} \right|g(y)dy = f(x)$$ -- 7.4 Two Related Operators -- 7.5 Generalized Solutions of Equations with Logarithmic Kernels -- 7.6 The Operator $$\int_{a}^{b} {(P(x - y)\ln \left| {x - y} \right| + | |
Q(x,y))g(y)dy}$$ -- 7.7 Disjoint Intervals of Integration -- 7.8 An Equation Over a Semi-Infinite Interval -- 7.9 The Equation of the Second Kind Over a Semi-Infinite Interval -- 7.10 Asymptotic Behavior of Eigenvalues -- 7.11 | |
Bibliographical Notes -- 7.12 Problems -- 8 Wiener-Hopf Integral Equations -- 8.1 Introduction -- 8.2 The Holomorphic Fourier Transform -- 8.3 The Mathematical Technique -- 8.4 The Distributional Wiener-Hopf Operators -- 8.5 | |
Illustrations -- 8.6 Bibliographical Notes -- 8.7 Problems -- 9 Dual and Triple Integral Equations -- 9.1 Introduction -- 9.2 The Hankel Transform -- 9.3 Dual Equations with Trigonometric Kernels -- 9.4 Beltrami’s Dual Integral | |
Equations -- 9.5 Some Triple Integral Equations -- 9.6 Erdélyi-Köber Operators -- 9.7 Dual Integral Equations of the Titchmarsh Type -- 9.8 Distributional Solutions of Dual Integral Equations -- 9.9 Bibliographical Notes -- 9.10 | |
Problems -- References | |
ISBN: | 9781461213826 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Applied mathematics , Engineering mathematics , Physics , Statistics , Mathematics , Analysis , Applications of Mathematics , Theoretical, Mathematical and Computational Physics , Statistical Theory and Methods |
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Call number: | SPRINGER-1999-9789401146074:ONLINE Show nearby items on shelf |
Title: | Limit Theorems for Random Fields with Singular Spectrum |
Author(s): |
Nikolai Leonenko |
Date: | 1999 |
Size: | 1 online resource (406 p.) |
Note: | 10.1007/978-94-011-4607-4 |
Contents: | 1 Second-Order Analysis of Random Fields -- 1.1 Basic Concepts and Notation -- 1.2 Elements of Spectral Theory of Random Fields -- 1.3 Models of Random Processes and Fields with Singular Spectrum -- 1.4 Tauberian and Abelian Theorems |
for Correlation Function of Homogeneous Isotropic Random Fields -- 2 Limit Theorems for Non-Linear Transformations of Random Fields -- 2.1 Some Properties of Gaussian and X-Squared Random Fields -- 2.2 Reduction Theorems for the Local | |
Functionals of Random Fields with Slowly Decaying Correlations -- 2.3 Multiple Stochastic Integrals -- 2.4 Non-Central Limit Theorems for Local Functionals of Random Fields -- 3 Asymptotic Distributions of Geometric Functionals of | |
Random Fields -- 3.1 Limit Distributions for Characteristics of the Excess above a Level for Gaussian Fields -- 3.2 Limiting Distributions for the Excess Over a Radial Surface of X-Squared Random Fields -- 3.3 Spherical Measures of | |
Excess over of Moving Level -- 3.4 Sojourns of Multi-Dimensional Gaussian Fields with Dependent Components -- 3.5 Asymptotic Normality of Random ‘Area of Surface’ of Planar Gaussian Field -- 3.6 Asymptotics for Occupation Densities of | |
Gaussian and X-Squared Random Fields -- 4 Limit Theorems For Solutions of The Burgers’ Equation with Random Data -- 4.1 Physical Motivation and Recent History -- 4.2 Hopf-Cole Solution -- 4.3 Parabolic Asymptotics for Weakly Dependent | |
Random Data: the Gaussian Scenario -- 4.4 Parabolic Limits for Strongly Dependent Random Initial Conditions: the Gaussian Scenario -- 4.5 Parabolic Limits for Strongly Dependent Random Data: the Non-Gaussian Scenario -- 4.6 Exact | |
Parabolic Asymptotics for Singular Burgers’ Equation -- 4.7 Hyperbolic Asymptotics for Rescaled Solutions of Burgers’ Equation -- 5 Statistical Problems for Random Fields with Singular Spectrum -- 5.1 Estimation of Mathematical | |
Expectation -- 5.2 Estimation of the Covariance Function -- 5.3 Efficient Estimation of Regression Coefficients of a Random Fields Observed on the Sphere -- 5.4 Estimation in the Frequency Domain -- Comments | |
ISBN: | 9789401146074 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 465 |
Keywords: | Mathematics , Applied mathematics , Engineering mathematics , Probabilities , Fluids , Statistics , Mathematics , Probability Theory and Stochastic Processes , Statistics, general , Fluid- and Aerodynamics , Applications of Mathematics |
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Call number: | SPRINGER-1999-9783662039328:ONLINE Show nearby items on shelf |
Title: | The Theory of Quark and Gluon Interactions |
Author(s): |
Francisco J Ynduráin |
Date: | 1999 |
Size: | 1 online resource (413 p.) |
Note: | 10.1007/978-3-662-03932-8 |
Contents: | 1. Generalities -- 2. QCD as a Field Theory -- 3. Renormalization in QCD -- 4. Perturbative QCD, I. Deep Inelastic Processes -- 5. Perturbative QCD, II. OZI Forbidden Decays Drell—Yan Processes Jets SVZ Sum Rules Exclusive Processes |
and so on. -- 6. Hadrons as Bound States of Quarks -- 7. Light Quarks PCAC Chiral Dynamics the QCD Vacuum -- 8. Instantons -- 9. Lattice QCD -- 10. The Perturbative QCD Series. The Parameters of QCD -- Appendices -- Appendix B: Some | |
Useful Integrals -- Appendix C: Group-theoretic Quantities. Group Integration -- Appendix D: Feynman Rules for QCD 383 Appendix E: Feynman Rules for Composite Operators -- Appendix F: Some Singular Functions -- Appendix G: Kinematics, | |
Cross Sections, Decay Rates. Units -- Appendix H: Functional Derivatives -- Appendix I: Gauge Invariant Operator Product -- References | |
ISBN: | 9783662039328 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Nuclear physics , Heavy ions , Hadrons , Elementary particles (Physics) , Quantum field theory , Physics , Elementary Particles, Quantum Field Theory , Mathematical Methods in Physics , Nuclear Physics, Heavy Ions, Hadrons |
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Call number: | SPRINGER-1999-9783642602184:ONLINE Show nearby items on shelf |
Title: | Computer Algebra in Scientific Computing CASC’99 Proceedings of the Second Workshop on Computer Algebra in Scientific Computing, Munich, May 31 – June 4, 1999 |
Author(s): | |
Date: | 1999 |
Size: | 1 online resource (511 p.) |
Note: | 10.1007/978-3-642-60218-4 |
Contents: | Solution of Ordinary Differential Equations with MathLie -- Analysis of Stability of Rational Approximations through Computer Algebra -- An Automatic Symbolic-Numeric Taylor Series ODE Solver -- About Normal Form Method -- Computer |
Algebra Investigation of Equivalence in 4-node Plane Stress/Strain Finite Elements -- Symmetry Theorems for the Newtonian 4- and 5-body Problems with Equal Masses -- Symbolic Derivation of Different Class of High-order Compact Schemes | |
for Partial Differential Equations -- Implementation of Aerodynamic Computations with Mathematica -- Completion of Linear Differential Systems to Involution -- Constrained Hamiltonian Systems and Gröbner Bases -- Construction of | |
Involutive Monomial Sets for Different Involutive Divisions -- Partial Inverse Heuristic for the Approximate Solution of Non-linear Equations -- Computing Cocycles on Simplicial Complexes -- Bifurcations of Maps in the Software Package | |
CONTENT -- Extending a Java Based Framework for Scientific Software-Components -- Symbolic-numeric Investigations for Stability Analysis of Satellite Systems -- Quantization by Presentation: The Nambu-Goto String in 1+3 Dimensions -- | |
One Algorithm of Finding Solutions for the Systems with First Integrals -- Cohomology of Lie Superalgebras of Hamiltonian Vector Fields: Computer Analysis -- Computer Algebra Tools in Construction of Renormgroup Symmetries 251 -- Where | |
Numerics Can Benefit from Computer Algebra in Finite Difference Modelling of Fluid Flows -- Effectively Computation of Some Radicals of Submodules of Free Modules -- Computations on Character Tables of Association Schemes -- | |
Investigation of Subgroup Embeddings by the Computer Algebra Package GAP -- An Investigation into Stability of Conservative Mechanical Systems Using Analytic Calculations -- Superfast Computations with Singular Structured Matrices over | |
Abstract Fields -- From Modeling to Simulation with Symbolic Computation: An Application to Design and Performance Analysis of Complex Optical Devices -- A Symbolic Numeric Environment for Analyzing Measurement Data in Multi-Model | |
Settings (Extended Abstract) -- Geometric Interpretation of Strong Inconsistency in Knowledge Based Systems -- Indices and Solvability for General Systems of Differential Equations -- Decomposing Systems of Polynomial Equations -- | |
Polynomials with Coefficients of Limited Accuracy -- Localization of Roots of a Polynomial not Represented in Canonical Form -- On Normalization of a Class of Polynomial Hamiltonians: From Ordinary and Inverse Points of View -- On | |
Multivariate Polynomial Decomposition -- Complexity of Monomial Evaluations and Duality -- On the Simplification of Nonlinear DAE Systems in Analog Circuit Design -- Symbolic Analysis of Computational Algorithms with SYDNA | |
ISBN: | 9783642602184 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algorithms , Mathematics , Algorithms , Algorithm Analysis and Problem Complexity |
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Call number: | SPRINGER-1999-9783034887458:ONLINE Show nearby items on shelf |
Title: | Mathematical Results in Quantum Mechanics QMath7 Conference, Prague, June 22–26, 1998 |
Author(s): | |
Date: | 1999 |
Size: | 1 online resource (398 p.) |
Note: | 10.1007/978-3-0348-8745-8 |
Contents: | I Plenary talks -- An adiabatic theorem without a gap condition -- Two-dimensional periodic Pauli operator. The effective masses at the lower edge of the spectrum -- Spectral problems in the theory of photonic crystals -- Optimal |
eigenvalues for some Laplacians and Schrödinger operators depending on curvature -- The spectral shift operator -- On the scattering operator for the Schrödinger equation with a time-dependent potential -- H_2-construction and some | |
applications -- Scattering with time periodic potentials and cyclic states -- Some geometry related to decay properties of the resolvent of a class of symmetric operators -- On some asymptotic formulas in the strong localization regime | |
of the theory of disordered systems -- Spectral measures and category -- Quantum dots. A survey of rigorous results -- II Session talks -- A simple model of concentrated nonlinearity -- Anomalous electron trapping by magnetic flux | |
tubes and electric current vortices -- On the absolutely continuous energy distribution of a quantum mechanical system in a bounded domain -- Some aspects of generalized contact interaction in one-dimensional quantum mechanics -- | |
Traces and trace norms for semigroup differences.. -- About a resolvent formula -- The determinant anomaly in low-dimensional quantum systems -- Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation -- | |
Coexistence of different spectral types for almost periodic Schrödinger equations in dimension one -- Dynamical localization for random Schrödinger operators and an application to the almost Mathieu operator -- On fractal structure of | |
the spectrum for periodic point perturbations of the Schrödinger operator with a uniform magnetic field -- A Weyl-Berry formula for the scattering operator associated to self-similar potentials on the line -- Localization and Lifshitz | |
tails for random quantum waveguides -- Birman-Schwinger analysis for bound states in a pair of parallel quantum waveguides with a semitransparent boundary -- On the absolute continuity of spectra of periodic elliptic operators -- Hardy | |
inequalities for magnetic Dirichlet forms -- Adiabatic curvature, chaos and the deformation of Riemann surfaces -- Operator interpretation of resonances arising in spectral problems for 2 x 2 matrix Hamiltonians -- On the operator-norm | |
convergence of the Trotter-Kato product formula -- A particular case of the inverse problem for the Sturm-Liouville equation with parameter dependent potential -- One-dimensional Schrödinger operators with decaying potentials -- | |
Stability of limiting absorption under singular perturbations -- Existence of averaging integrals for self-adjoint operators -- Monotonicity versus non-monotonicity in random operators -- A model in perturbation theory -- Band gap of | |
the spectrum in periodically curved quantum waveguides -- A list of other talks -- A list of participants | |
ISBN: | 9783034887458 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory Advances and Applications : 108 |
Keywords: | Mathematics , Mathematical physics , Mechanics , Mathematics , Mathematical Physics , Mechanics |
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Call number: | SPRINGER-1999-9783034887281:ONLINE Show nearby items on shelf |
Title: | Probabilistic Behavior of Harmonic Functions |
Author(s): |
Rodrigo Bañuelos |
Date: | 1999 |
Size: | 1 online resource (209 p.) |
Note: | 10.1007/978-3-0348-8728-1 |
Contents: | 1 Basic Ideas and Tools -- 1.1 Harmonic functions and their basic properties -- 1.2 The Poisson kernel and Dirichlet problem for the ball -- 1.3 The Poisson kernel and Dirichlet problem for R+n+1 -- 1.4 The Hardy-Littlewood and |
nontangential maximal functions -- 1.5 HP spaces on the upper half space -- 1.6 Some basics on singular integrals -- 1.7 The g-function and area function -- 1.8 Classical results on boundary behavior -- 2 Decomposition into | |
Martingales: An Invariance Principle -- 2.1 Square function estimates for sums of atoms -- 2.2 Decomposition of harmonic functions -- 2.3 Controlling errors: gradient estimates -- 3 Kolmogorov’s LIL for Harmonic Functions -- 3.1 The | |
proof of the upper-half -- 3.2 The proof of the lower-half -- 3.3 The sharpness of the Kolmogorov condition -- 3.4 A related LIL for the Littlewood-Paley g*-function -- 4 Sharp Good-? Inequalities for A and N -- 4.1 Sharp control of N | |
by A -- 4.2 Sharp control of A by N -- 4.3 Application I. A Chung-type LIL for harmonic functions -- 4.4 Application II. The Burkholder-Gundy ?-theorem -- 5 Good-? Inequalities for the Density of the Area Integral -- 5.1 Sharp control | |
of A and N by D -- 5.2 Sharp control of D by A and N -- 5.3 Application I. A Kesten-type LIL and sharp LP-constants -- 5.4 Application II. The Brossard-Chevalier L log L result -- 6 The Classical LIL’s in Analysis -- 6.1 LIL’s for | |
lacunary series -- 6.2 LIL’s for Bloch functions -- 6.3 LIL’s for subclasses of the Bloch space -- 6.4 On a question of Makarov and Przytycki -- References -- Notation Index | |
ISBN: | 9783034887281 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics : 175 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Probabilities , Mathematics , Probability Theory and Stochastic Processes , Analysis |
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Call number: | SPRINGER-1999-9783034886857:ONLINE Show nearby items on shelf |
Title: | Applications and Computation of Orthogonal Polynomials Conference at the Mathematical Research Institute Oberwolfach, Germany March 22–28, 1998 |
Author(s): | |
Date: | 1999 |
Size: | 1 online resource (273 p.) |
Note: | 10.1007/978-3-0348-8685-7 |
Contents: | The sensitivity of least squares polynomial approximation -- Transpose-free look-ahead algorithms for Lanczos’ method -- Applications of anti-Gauss quadrature rules in linear algebra -- Stieltjes polynomials and the error of |
Gauss-Kronrod quadrature formulas -- Fast solution of confluent Vandermonde-like linear systems using polynomial arithmetic -- On discrete polynomial least-squares approximation in moving time windows -- Quadrature rules based on | |
s-orthogonal polynomials for evaluating integrals with strong singularities -- Gegenbauer weight functions admitting L2 Duffin and Schaeffer type inequalities -- Questions related to Gaussian quadrature formulas and two-term recursions | |
-- Construction and computation of a new set of orthogonal polynomials -- Fourier transforms of orthogonal polynomials of singular continuous spectral measures -- On a sequence of fast decreasing polynomial operators -- Müntz | |
orthogonal polynomials and their numerical evaluation -- Positivity of Gauss-Kronrod formulae for a certain ultraspherical weight function -- A Christoffel-Darboux-type formula for Szegö polynomials and polynomial evaluation -- | |
Applications of tensor-valued tri-variate Hermite polynomials and spherical harmonics in the kinetic theory of gases -- Indeterminate moment problems and a conjecture on the growth of the entire functions in the Nevanlinna | |
parametrization -- Spectral methods based on nonclassical orthogonal polynomials -- Author index | |
ISBN: | 9783034886857 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | International Series of Numerical Mathematics : 131 |
Keywords: | Engineering , Mathematical analysis , Analysis (Mathematics) , Applied mathematics , Engineering mathematics , Engineering , Appl.Mathematics/Computational Methods of Engineering , Analysis , Applications of Mathematics |
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Call number: | SPRINGER-1999-9781461332763:ONLINE Show nearby items on shelf |
Title: | Partial Differential and Integral Equations |
Author(s): | |
Date: | 1999 |
Size: | 1 online resource (384 p.) |
Note: | 10.1007/978-1-4613-3276-3 |
Contents: | 1 Gauss-Manin Connexion of Curve Singularities -- 2 Group Convolution Operators on Step of Two Nilpotent Lie Groups -- 3 Some Boundary Value Problems for Second Order Overdetermined Elliptic Systems in the Unit Ball of ?n -- 4 |
Riemann-Hilbert Boundary Value Problems in ?n -- 5 The Riemann-Hilbert Problem for Nonlinear Elliptic Complex Equations of First Order in Multiply Connected Infinite Domains -- 6 The Riemann-Hilbert Problem for First Order Complex | |
Equations of Mixed Type -- 7 On Totally Real Non-Compact Manifolds Globally Foliated by Analytic Discs -- 8 Boundary Behaviour of Vector-Valued Functions of Two Classes in Locally Convex Spaces -- 9 On Singular Integrals of the | |
Time-Harmonic Maxwell Equations Theory -- 10 Systems of First Order Partial Differential Equations — a Hypercomplex Approach -- 11 To Elliptic Theory for Domains with Piecewise Smooth Boundary in the Plane -- 12 Boundary Value Problems | |
for a System of First Order Equations of a Principal Type in the Plane -- 13 The Stability of the Riemann Boundary Value Problem for Vector-Valued M-Analytic Functions -- 14 A Class of Inverse Hilbert Boundary Value Problems -- 15 | |
Cauchy Formula, Integral of Cauchy Type and Hilbert Problem for Bianalytic Functions -- 16 On Uniqueness Conditions for Entire Polyharmonic Functions -- 17 Bi-Analytic Functions and Their Applications in Elasticity -- 18 Effect of | |
Periodic Gasket on a Periodic Contact Problem -- 19 Singular Integral Operators and Singular Quadrature Operators for Singular Integral Equations with Hilbert Kernel -- 20 Some Co-Circular Crack Problems with Cyclic Symmetry -- 21 The | |
Oblique Derivative Problem for Nonlinear Parabolic Equations of Second Order with Measurable Coefficients in a Higher Dimensional Domain -- 22 Existence and Uniqueness for Boundary Value Contact Problems -- 23 Weakly Hyperbolic | |
Equations — a Modern Field in the Theory of Hyperbolic Equations -- 24 Eigenvalue Problems for Elliptic Type Partial Differential Operators with Spectral Parameter Contained Linearly in Boundary Conditions -- 25 On Indefinite Nonlinear | |
Neumann Problems -- 26 Higher Order Ordinary Differential Equations with Super-Singular Points -- 27 Applications of Methods of Integrals and Function Theory to Statistics | |
ISBN: | 9781461332763 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | International Society for Analysis, Applications and Computation: 2 |
Keywords: | Mathematics , Functions of complex variables , Integral transforms , Operational calculus , Partial differential equations , Functions of real variables , Mathematics , Partial Differential Equations , Integral Transforms, Operational Calculus , Functions of a Complex Variable , Several Complex Variables and Analytic Spaces , Real Functions |
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Call number: | SPRINGER-1999-9781461222361:ONLINE Show nearby items on shelf |
Title: | Analysis of Divergence Control and Management of Divergent Processes |
Author(s): | |
Date: | 1999 |
Size: | 1 online resource (568 p.) |
Note: | 10.1007/978-1-4612-2236-1 |
Contents: | Overview -- I Convergence and Summability -- 1 Tauberian theorems for generalized Abelian summability methods -- 2 Series summability of complete biorthogonal sequences -- 3 Growth of Cesàro means of double Vilenkin-Fourier series of |
unbounded type -- 4 A substitute for summability in wavelet expansions -- 5 Expansions in series of Legendre functions -- 6 Endpoint convergence of Legendre series -- 7 Inversion of the horocycle transform on real hyperbolic spaces via | |
a wavelet-like transform -- 8 Fourier-Bessel expansions with general boundary conditions -- II Singular Integrals and Multipliers -- 9 Convolution Calderón-Zygmund singular integral operators with rough kernels -- 10 Haar multipliers, | |
paraproducts, and weighted inequalities -- 11 Multipliers and square functions for Hp spaces over Vilenkin groups -- 12 Spectra of pseudo-differential operators in the Hörmander class -- 13 Scaling properties of infinitely flat curves | |
and surfaces -- 14 Some Lp(L?)- and L2(L2)- estimates for oscillatory Fourier transforms -- 15 Optimal spaces for the S’-convolution with the Marcel Riesz kernels and the N-dimensional Hilbert kernel -- III Integral Operators and | |
Functional Analysis -- 16 Asymptotic expansions and linear wavelet packets on certain hypergroups -- 17 Hardy-type inequalities for a new class of integral operators -- 18 Regularly bounded functions and Hardy’s inequality -- 19 | |
Extremal problems in generalized Sobolev classes -- 20 On angularly perturbed Laplace equations in the unit ball and their distributional boundary values -- 21 Nonresonant semilinear equations and applications to boundary value | |
problems -- 22 A topological and functional analytic approach to statistical convergence -- IV Asymptotics and Applications -- 23 Optimal control of divergent control systems -- 24 Surfaces minimizing integrals of divergent integrands | |
-- 25 Sparse exponential sums with low sidelobes -- 26 Spline type summability for multivariate sampling -- 27 B-Splines and orthonormal sets in Paley-Wiener space -- 28 Norms of powers and a central limit theorem -- 29 | |
Quasiasymptotics at zero and nonlinear problems in a framework of Colombeau generalized functions | |
ISBN: | 9781461222361 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Applied mathematics , Engineering mathematics , Mathematics , Applications of Mathematics , Signal, Image and Speech Processing , Functional Analysis |
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