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Call number: | 9783319393391:ONLINE Show nearby items on shelf |
Title: | Singularities in Geometry, Topology, Foliations and Dynamics A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014 |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (XVII, 231 p. 15 illus., 10 illus. in color p.) |
Contents: | Extending the action of Schottky groups on the complex anti-de Sitter space to the projective space -- Puiseux Parametric Equations via the Amoeba of the Discriminant -- Some open questions on arithmetic Zariski pairs -- Logarithmic |
vector fields and the Severi strata in the discriminant -- Classification of Isolated Polar Weighted Homogeneous Singularities -- Rational and iterated maps, degeneracy loci, and the generalized Riemann-Hurwitz formula -- On singular | |
varieties with smooth subvarieties -- On Polars of Plane Branches -- Singular Intersections of Quadrics I -- A New Conjecture, a New Invariant, and a New Non-splitting Result -- Lipschitz geometry does not determine embedded | |
topological type -- Projective transverse structures for some foliations -- Chern classes and transversality for singular spaces | |
ISBN: | 9783319393391 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Algebraic geometry , Global analysis (Mathematics) , Manifolds (Mathematics) , Functions of complex variables , Mathematics , Several Complex Variables and Analytic Spaces , Algebraic Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | 9781493965724:ONLINE Show nearby items on shelf |
Title: | Statistics and Analysis of Scientific Data |
Author(s): |
Massimiliano Bonamente |
Date: | 2017 |
Edition: | 2nd ed. 2017 |
Size: | 1 online resource (XVII, 318 p. 40 illus., 4 illus. in color p.) |
Contents: | Theory of Probability -- Random Variables and Their Distribution -- Sum and Functions of Random Variables -- Estimate of Mean and Variance and Confidence Intervals -- Median, Weighted Mean and Linear Average (NEW) -- Distribution |
Function of Statistics and Hypothesis Testing -- Maximum Likelihood Fit to a Two-Variable Dataset -- Goodness of Fit and Parameter Uncertainty -- Systematic Errors and Intrinsic Scatter (NEW) -- Fitting Data with Bivariate Errors (NEW) | |
-- Comparison Between Models -- Monte Carlo Methods -- Markov Chains and Monte Carlo Markov Chains -- Statistics for Business Sciences and Addition of Multi–Variate Analysis (NEW) | |
ISBN: | 9781493965724 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Physics , System theory , Statistics , Applied mathematics , Engineering mathematics , Physics , Mathematical Methods in Physics , Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Scien , Statistics for Business/Economics/Mathematical Finance/Insurance , Appl.Mathematics/Computational Methods of Engineering , Complex Systems , Statistical Physics and Dynamical Systems |
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Call number: | SPRINGER-2016-9783319338774:ONLINE Show nearby items on shelf |
Title: | Spectral Theory of Infinite-Area Hyperbolic Surfaces |
Author(s): |
David Borthwick |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (37 p.) |
Note: | 10.1007/978-3-319-33877-4 |
Contents: | Introduction -- Hyperbolic Surfaces -- Selberg Theory for Finite-Area Hyperbolic Surfaces -- Spectral Theory for the Hyperbolic Plane -- Model Resolvents for Cylinders -- The Resolvent -- Spectral and Scattering Theory -- Resonances and Scattering Poles -- Growth Estimates and Resonance Bounds -- Selberg Zeta Function -- Wave Trace and Poisson Formula -- Resonance Asymptotics -- Inverse Spectral Geometry -- Patterson-Sullivan Theory -- Dynamical Approach to the Zeta Function -- Numerical Computatio ns -- Appendix -- References -- Notation Guide -- Index |
ISBN: | 9783319338774 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics: 318 |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Partial differential equations , Hyperbolic geometry , Physics , Mathematics , Functional Analysis , Partial Differential Equations , Functions of a Complex Variable , Hyperbolic Geometry , Mathematical Methods in Physics |
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Call number: | SPRINGER-2016-9783319323152:ONLINE Show nearby items on shelf |
Title: | Hyperbolicity of Projective Hypersurfaces |
Author(s): |
Simone Diverio |
Date: | 2016 |
Size: | 1 online resource (89 p.) |
Note: | 10.1007/978-3-319-32315-2 |
Contents: | - Introduction -- Kobayashi hyperbolicity: basic theory -- Algebraic hyperbolicity -- Jets spaces -- Hyperbolicity and negativity of the curvature -- Hyperbolicity of generic surfaces in projective 3-space -- Algebraic degeneracy for projective hyp ersurfaces |
ISBN: | 9783319323152 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | IMPA Monographs : 5 |
Keywords: | Mathematics , Algebraic geometry , Functions of complex variables , Differential geometry , Mathematics , Differential Geometry , Algebraic Geometry , Several Complex Variables and Analytic Spaces |
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Call number: | SPRINGER-2016-9783319290461:ONLINE Show nearby items on shelf |
Title: | Measure and Integration |
Author(s): |
Hari Bercovici |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (300 p.) |
Note: | 10.1007/978-3-319-29046-1 |
Contents: | Rings of sets -- Measurability -- Integrals and Measures -- Convergence Theorems for Lebesgue Integrals -- Existence and Uniqueness of Measures -- Signed Measures, Complex Measures and Absolute Continuity -- Measure and Topology -- Product Measures -- The Lp Spaces -- Fourier Analysis -- Standard Measure Spaces. |
ISBN: | 9783319290461 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Measure theory , Functions of real variables , Mathematics , Measure and Integration , Real Functions |
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Call number: | SPRINGER-2016-9783319290003:ONLINE Show nearby items on shelf |
Title: | Divergent Series, Summability and Resurgence III Resurgent Methods and the First Painlevé Equation |
Author(s): |
Eric Delabaere |
Date: | 2016 |
Size: | 1 online resource (14 p.) |
Note: | 10.1007/978-3-319-29000-3 |
Contents: | Avant-Propos -- Preface to the three volumes -- Preface to this volume -- Some elements about ordinary differential equations -- The first Painlevé equation -- Tritruncated solutions for the first Painlevé equation -- A step beyond Borel-Laplace summability -- Transseries and formal integral for the first Painlevé equation -- Truncated solutions for the first Painlevé equation -- Supplements to resurgence theory -- Resurgent structure for the first Painlevé equation -- Index |
ISBN: | 9783319290003 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2155 |
Keywords: | Mathematics , Functions of complex variables , Differential equations , Sequences (Mathematics) , Special functions , Mathematics , Sequences, Series, Summability , Ordinary Differential Equations , Functions of a Complex Variable , Special Functions |
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Call number: | SPRINGER-2016-9783319263090:ONLINE Show nearby items on shelf |
Title: | Boundary Integral Equation Methods and Numerical Solutions Thin Plates on an Elastic Foundation |
Author(s): |
Christian Constanda |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (196 p.) |
Note: | 10.1007/978-3-319-26309-0 |
Contents: | Preface -- 1. The Mathematical Model -- 2. The Layer Potentials -- 3. Existence of Solutions -- 4. Software Development -- 5. Computational Examples -- References -- Index |
ISBN: | 9783319263090 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Developments in Mathematics: 35 |
Keywords: | Mathematics , Functions of complex variables , Integral equations , Partial differential equations , Mathematics , Integral Equations , Partial Differential Equations , Functions of a Complex Variable |
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Call number: | SPRINGER-2016-9783319247113:ONLINE Show nearby items on shelf |
Title: | Dessins d'Enfants on Riemann Surfaces |
Author(s): |
Gareth A Jones |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (259 p.) |
Note: | 10.1007/978-3-319-24711-3 |
Contents: | Historical and introductory background -- Graph embeddings -- Dessins and triangle groups -- Galois actions -- Quasiplatonic surfaces, and automorphisms -- Regular maps -- Regular embeddings of complete graphs -- Wilson operations -- Further exampl es -- Arithmetic aspects -- Beauville surfaces |
ISBN: | 9783319247113 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algebraic geometry , Group theory , Functions of complex variables , Hyperbolic geometry , Mathematics , Algebraic Geometry , Group Theory and Generalizations , Functions of a Complex Variable , Several Complex Variables and Analytic Spaces , Hyperbolic Geometry |
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Call number: | SPRINGER-2016-9783034809641:ONLINE Show nearby items on shelf |
Title: | Application of Holomorphic Functions in Two and Higher Dimensions |
Author(s): |
Klaus Gürlebeck |
Date: | 2016 |
Size: | 1 online resource (3 p.) |
Note: | 10.1007/978-3-0348-0964-1 |
Contents: | 1.Basic Properties of Holomorphic Functions -- 2.Conformal and Quasi-conformal Mappings -- 3.Function Theoretic Function spaces -- 4.Operator Calculus -- 5.Decompositions -- 6.Some First Order Systems of Partial Differential Equations -- 7.Boundary Value Problems of Second Order Partial Differential Equations -- 8.Some Initial-boundary Value Problems -- 9.Riemann-Hilbert Problems -- 10.Initial Boundary Value Problems on the Sphere -- 11.Fourier Transforms -- Bibliography -- Index |
ISBN: | 9783034809641 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Integral transforms , Operational calculus , Partial differential equations , Mathematics , Integral Transforms, Operational Calculus , Functions of a Complex Variable , Partial Differential Equations , Functional Analysis |
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Call number: | SPRINGER-2014-9788847055018:ONLINE Show nearby items on shelf |
Title: | Elementi di Analisi Complessa [electronic resource] : Funzioni di una variabile |
Author(s): |
Carlo Presilla |
Date: | 2014 |
Edition: | 2a edizione |
Publisher: | Milano : Springer Milan : Imprint: Springer |
Size: | 1 online resource |
Note: | Questo testo, giunto alla seconda edizione, adatto per una prima esposizione della teoria delle funzioni di singola variabile complessa e si rivolge a studenti di Fisica, Matematica e Ingegneria che abbiano acquisito lenozioni fondamentali dellAnali si Matematica reale. Lesigenza di una nuova pubblicazione nasce dallidea di effettuare una selezione di argomenti, ritenuti fondamentali, la cui esposizione risulti sistematica e autoconsistentein circa 60 ore di lezione mantenendo, al tempo stesso, il ri gore matematico volto a favorire la maturazione scientifica dello studente e prepararlo alla lettura di testi avanzati. A corredo della trattazione teorica vengono proposticirca 250 esercizi, raccolti tra le prove scritte assegnate per il superamento del corso, tutti forniti di soluzione dettagliata. Il loro svolgimento costituisce una parte imprescindibile per lacquisizione della materia |
Contents: | 1 Numeri complessi |
2 Spazi metrici | |
3 Limiti e continuit | |
4 Successioni e serie di funzioni | |
5 Derivate e funzioni analitiche | |
6 Funzioni elementari | |
7 Integrali | |
8 Serie di Taylor e Laurent | |
9 Residui | |
10 Applicazioni dei residui | |
11 Ulteriori propriet delle funzioni analitiche | |
Appendice A. Soluzione degli esercizi proposti | |
ISBN: | 9788847055018 |
Series: | eBooks |
Series: | SpringerLink |
Series: | UNITEXT, 2038-5714 : v72 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2014-9784431545712:ONLINE Show nearby items on shelf |
Title: | Nevanlinna Theory in Several Complex Variables and Diophantine Approximation [electronic resource] |
Author(s): |
Junjiro Noguchi Jrg Winkelmann |
Date: | 2014 |
Publisher: | Tokyo : Springer Japan : Imprint: Springer |
Size: | 1 online resource |
Note: | The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with ninechapters systematically de scribes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 tothe current state of research. Chapter 2 present s the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension isdescribed. In Chap. 3 the Second Main Theorem for differentiably non-d egenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem forentire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Ca rtan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraicvarieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of N oguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to thenotion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are dis cussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt withfrom the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is d iscussed. Finally, in Chap. 9, the theorems of Roth, Schmidt,Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, |
Contents: | Nevanlinna Theory of Meromorphic Functions |
First Main Theorem | |
Differentiably Non | |
Degenerate Meromorphic Maps | |
Entire Curves into Algebraic Varieties | |
Semi | |
Abelian Varieties | |
Entire Curves into Semi | |
Abelian Varieties | |
Kobayashi Hyperbolicity | |
Nevanlinna Theory over Function Fields | |
Diophantine Approximation | |
Bibliography | |
Index | |
Symbols | |
ISBN: | 9784431545712 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v350 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Functions of complex variables , Differential equations, partial , Number theory |
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Call number: | SPRINGER-2014-9783642541247:ONLINE Show nearby items on shelf |
Title: | Mathematics for Physicists and Engineers [electronic resource] : Fundamentals and Interactive Study Guide |
Author(s): |
Klaus Weltner Sebastian John Wolfgang J Weber Peter Schuster Jean Grosjean |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This textbook offers an accessible and highly approved approach which is characterized by the combination of the textbook with a detailed study guide available online at our repository extras.springer.com. This study guide dividesthe whole learning t ask into small units which the student is very likely to master successfully. Thus he or she is asked to read and study a limited section of the textbook and to return to the study guide afterwards. Working with thestudy guide his or her learning results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. Since the degree of difficulties is slowlyrising the students gain confidence and experience their own prog ress in mathematical competence thus fostering motivation. Furthermore in case of learning difficulties he or she is given supplementary explanations and in case ofindividual needs supplementary exercises and applications. So the sequence of the studies i s individualized according to the individual performance and needs and can be regarded as full tutorial course. The study guide satisfies twoobjectives simultaneously: firstly it enables students to make effective use of the textbook and secondly it offer s advice on the improvement of study skills. Empirical studies have shown that the student's competence for using writteninformation has improved significantly by using this study guide. The new edition includes a new chapter on Fourier integrals and Four ier transforms, numerous sections had been updated, 30 new problems with solutions had been added.The interactive study guide has seen a substantial update |
Contents: | From the Contents: Vector Algebra I: Scalars and Vectors |
Vector Algebra II: Scalar and Vector Products | |
Functions | |
Exponential, Logarithmic and Hyperbolic Functions | |
Differential Calculus | |
Integral Calculus | |
Applications of Integration | |
Taylor Series and Power Series | |
Complex Numbers | |
Differential Equations | |
Laplace Transforms | |
Functions of Several Variables Partial Differentiation and Total Differentiation | |
Multiple Integrals Coordinate Systems | |
Transformation of Coordinates Matrices | |
Sets of Linear Equations Determinanats | |
Eigenvalues and Eigenvectors of R | |
ISBN: | 9783642541247 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Chemistry , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2014-9783319062099:ONLINE Show nearby items on shelf |
Title: | From Real to Complex Analysis [electronic resource] |
Author(s): |
R. H Dyer D. E Edmunds |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis andtopology. Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectednessand various forms of homotopy. The final chapter d evelops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using theapproach due to Dixon. Special features are the inclusion of proofs of M ontel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included ineach of the chapters, detailed solutions of the majority of which are given at the end. From Re al to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding inanalysis in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be mad e |
Contents: | The Riemann integral |
Metric spaces | |
Complex Analysis | |
Sets and functions | |
ISBN: | 9783319062099 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables |
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Call number: | SPRINGER-2014-9783319051109:ONLINE Show nearby items on shelf |
Title: | Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis [electronic resource] |
Author(s): |
Daniel Alpay Maria Elena Luna-Elizarrars Michael Shapiro Daniele C Struppa |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers, and then defines the notion of bicomplex modules. Afterintroducing a number o f norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this mayserve for many different developments, just like the usual functional analysis with complex scalars, and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schuranalysis |
Contents: | 1. Bicomplex and hyperbolic numbers |
2. Bicomplex functions and matrices | |
3. BC | |
modules | |
4. Norms and inner products on BC | |
modules | |
5. Linear functionals and linear operators on BC | |
modules | |
6. Schur analysis | |
ISBN: | 9783319051109 |
Series: | eBooks |
Series: | SpringerLink |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Operator theory , Systems theory |
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Call number: | SPRINGER-2014-9783319031736:ONLINE Show nearby items on shelf |
Title: | Lectures on Mappings of Finite Distortion [electronic resource] |
Author(s): |
Stanislav Hencl Pekka Koskela |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | In this book we introduce the class of mappings of finite distortion as a generalization of the class of mappings of bounded distortion. Connections with models of nonlinear elasticity are also discussed. We study continuityproperties, behavior of ou r mappings on null sets, topological properties like openness and discreteness, regularity of the potential inverse mappings and many other aspects |
Contents: | Introduction |
Continuity | |
Openness and discreteness | |
Images and preimages of null sets | |
Homeomorphisms of finite distortion | |
Integrability of Jf and 1/Jf | |
Final comments | |
Appendix | |
References | |
ISBN: | 9783319031736 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2096 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Functions of complex variables , Differential equations, partial |
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Call number: | SPRINGER-2014-9783319020990:ONLINE Show nearby items on shelf |
Title: | Introduction to Partial Differential Equations [electronic resource] |
Author(s): |
Peter J Olver |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, andelsewhere. The exposition car efully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, andinclude straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material thatmotivates the student to delve further into the subject. No previous experien ce with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- andmulti-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to formthe core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximu m Principle, financial models, dispersion and solitons, Huygens' Principle, quantum mechanical systems,and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes ar e an important component of any introductory course, and the text covers the twomost basic approaches: finite differences and finite elements. Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests a re centered on the development of symmetry-based methodsfor differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research |
Contents: | What are Partial Differential Equations? |
Linear and Nonlinear Waves | |
Fourier Series | |
Separation of Variables | |
Finite Differences | |
Generalized Functions and Greens Functions | |
Complex Analysis and Conformal Mapping | |
Fourier Transforms | |
Linear and Nonlinear Evolution Equations | |
A General Framework forLinear Partial Differential Equations | |
FiniteElements and Weak Solutions | |
Dynamics of Planar Media | |
Partial Differential Equations in Space . | |
ISBN: | 9783319020990 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Differential equations, partial |
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Call number: | SPRINGER-2014-9783319018065:ONLINE Show nearby items on shelf |
Title: | Harmonic and Complex Analysis and its Applications [electronic resource] |
Author(s): |
Alexander Vasil'ev |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This volume highlights the main results of the research performed within the network Harmonic and Complex Analysis and its Applications (HCAA), which was a five-year (20072012) European Science Foundation Programmeintended to explore and to strengthe n the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. Itcoordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings,potential theory, Banach spaces of analytic functions and their applications to the problem s of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveyswritten as a result of activities of the Programme and will be interesting and useful for professionals and novi ces in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader willundoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme |
Contents: | L.D. Abreu, H.G. Feichtinger: Function spaces of polyanalytic functions |
F. Bracci, M.D. Contreras, S. Daz | |
Madrigal,A. Vasil'ev: Classical and stochastic Lwner | |
Kufarev equations | |
M. Elin, F. Jacobzon, M. Levenshtein, D. Shoikhet: The Schwarz Lemma. Rigidity and Dynamics | |
H.G. Feichtinger, M. Pap: Coorbit theory and Bergman spaces | |
S.J. Gardiner, T. Sjdin: Quadrature domains and their two | |
phase counterparts | |
B. Gustafsson: Exponential transforms, resultants and moments | |
M. Schlichenmaier: From the Virasoro Algebra to KricheverNovikov Type Algebras and Beyond | |
ISBN: | 9783319018065 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Functional analysis , Functions of complex variables , Potential theory (Mathematics) |
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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-2014-9783319002125:ONLINE Show nearby items on shelf |
Title: | Lectures on Complex Integration [electronic resource] |
Author(s): |
A. O Gogolin Elena G Tsitsishvili Andreas Komnik |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them intointegrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal ofthe book is to introduce the reader to this beaut iful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations.This is done with a help of numerous examples and problems with detailed solutions |
Contents: | Basics |
Hypergeometric series with applications | |
Integral equations | |
Orthogonal polynomials | |
Solutions to the problems | |
ISBN: | 9783319002125 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Undergraduate Lecture Notes in Physics, 2192-4791 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Functions of complex variables |
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Call number: | SPRINGER-2014-9783034806220:ONLINE Show nearby items on shelf |
Title: | Real Quaternionic Calculus Handbook [electronic resource] |
Author(s): |
Joo Pedro Morais Svetlin Georgiev Wolfgang Sprig |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, suchas complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysishas become a well established branch in ma thematics and has been greatly successful in many different directions. This book is based onconcrete examples and exercises rather than general theorems, thus making it suitable for anintroductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises atthe end of each chapter and its straightforward writing style the book addresses readers w ho have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis,ordinary differential equations, partial differential equations, and theory of distributions |
Contents: | 1 An introduction to quaternions |
2 Quaternions and spatial rotation | |
3 Quaternion sequences | |
4 Quaternion series and infinite products | |
5 Exponents and logarithms | |
6 Trigonometric functions | |
7 Hyperbolic functions | |
8 Inverse hyperbolic and trigonometric functions | |
9 Quaternion matrices | |
10 Monomials, polynomials and binomials | |
11 Solutions | |
Bibliography | |
Index | |
ISBN: | 9783034806220 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Algebra , Functions of complex variables , Combinatorics , Geometry |
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Call number: | SPRINGER-2014-9781493912551:ONLINE Show nearby items on shelf |
Title: | The Corona Problem [electronic resource] : Connections Between Operator Theory, Function Theory, and Geometry |
Author(s): |
Ronald G Douglas Steven G Krantz Eric T Sawyer Sergei Treil Brett D Wick |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | The purpose of the corona workshop was toconsider the corona problem in both one and several complex variables, both in the context of function theory and harmonic analysis as well as the context of operator theory andfunctional analysis. It was held in June 2012 at the Fields Institute in Toronto, and attended by about fifty mathematicians. This volume validates and commemorates the workshop, and records some of the ideas that were developedwithin. The corona problem dates back to 1941. It has exert ed a powerful influence over mathematical analysis for nearly 75 years. There is material to help bring people up to speed in the latest ideas of the subject, as well ashistorical material to provide background. Particularly noteworthy is a history of the corona problem, authored by the five organizers, that provides a unique glimpse at how the problem and its many different solutions have developed.There has never been a meeting of this kind, and there has never been a volume of this kind. Mathematicians both veterans and newcomerswill benefit from reading this book. This volume makes a unique contribution to the analysisliterature and will be a valuable part of the canon for many years to come |
Contents: | The History of the Corona Problem (R.G. Douglas, S.G. Krantz, E.T. Sawyer, S. Treil, B.D. Wick) |
Corona Problem for H^\infty on Riemann Surfaces (A. Brudnyi) | |
Connections of the Corona Problem with Operator Theory and Complex Geometry (R.G. Douglas) | |
On the Maximal Ideal Space of a Sarason | |
Type Algebra on the Unit Ball (J. Eschmeier) | |
A Subalgebra of the Hardy Algebra Relevant in Control Theory and its Algebraic | |
Analytic Properties (M. Frentz, A. Sasane) | |
The Corona Problem in Several Complex Variables (S.G. Krantz) | |
Corona | |
Type Theorems and Division in Some Function Algebras on Pl | |
ISBN: | 9781493912551 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Fields Institute Communications, 1069-5265 : v72 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2014-9781447164340:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods for Elastic Plates [electronic resource] |
Author(s): |
Christian Constanda |
Date: | 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers andaircraft. This book emplo ys two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process ofbending than Kirchhoffs classical one. The fi rst method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on thebasis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hlder continuous and Hlder continuously differentiable) functions. The second technique rewrites the differential system in terms ofcomplex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials. The last chapter develops a generalized Fourier series method closely connected with the structure of the system,which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure. Thepresentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students wit h a basic knowledge of advanced calculus |
Contents: | Singular Kernels |
Potentials and Boundary Integral Equations | |
Bending of Elastic Plates | |
The Layer Potentials | |
The Newtonian Potential | |
Existence of Regular Solutions | |
Complex Variable Treatment | |
Generalized Fourier Series | |
ISBN: | 9781447164340 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Integral equations , Materials |
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Call number: | SPRINGER-2014-9781447163954:ONLINE Show nearby items on shelf |
Title: | An Introduction to Laplace Transforms and Fourier Series [electronic resource] |
Author(s): |
Phil Dyke |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative.Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis onapplication with the necessary mathematical g rounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Onlyknowledge of elementary trigonometry and calculus are required as prereq uisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics ormathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems |
Contents: | The Laplace Transform |
Further Properties of the Laplace Transform | |
Convolution and the Solution of Ordinary Differential Equations | |
Fourier Series | |
Partial Differential Equations | |
Fourier Transforms | |
Wavelets and Signal Processing | |
Complex Variables and Laplace Transforms | |
ISBN: | 9781447163954 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functions of complex variables , Integral Transforms , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2013-9783642338717:ONLINE Show nearby items on shelf |
Title: | Regular Functions of a Quaternionic Variable [electronic resource] |
Author(s): |
Graziano Gentili Caterina Stoppato Daniele C Struppa |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The theory of slice regular functions over quaternions is the central subject of the present volume. This recent theory has expanded rapidly, producing a variety of new results that have caught the attention of the internationalresearch community. At the same time, the theory has already developed sturdy foundations. The richness of the theory of the holomorphic functions of one complex variable and its wide variety of applications are a strong motivation forthe study of its analogs in higher dimensi ons. In this respect, the four-dimensional case is particularly interesting due to its relevance in physics and its algebraic properties, as the quaternion forms the only associative realdivision algebra with a finite dimension n>2. Among other interestin g function theories introduced in the quaternionic setting, that of (slice) regular functions shows particularly appealing features. For instance, this class offunctions naturally includes polynomials and power series. The zero set of a slice regular func tion has an interesting structure, strictly linked to a multiplicative operation, and it allows the study of singularities. Integralrepresentation formulas enrich the theory and they are a fundamental tool for one of the applications, the construction of a noncommutative functional calculus. The volume presents a state-of-the-art survey of the theory and a briefoverview of its generalizations and applications. It is intended for graduate students and researchers in complex or hypercomplex analysis and geo metry, function theory, and functional analysis in general |
Note: | Springer eBooks |
Contents: | Introduction |
1.Definitions and Basic Results | |
2.Regular Power Series | |
3.Zeros | |
4.Infinite Products | |
5.Singularities | |
6.Integral Representations | |
7.Maximum Modulus Theorem and Applications | |
8.Spherical Series and Differential | |
9.Fractional Transformations and the Unit Ball | |
10.Generalizations and Applications | |
Bibliography | |
Index | |
ISBN: | 9783642338717 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Sequences (Mathematics) |
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Call number: | SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf |
Title: | Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations |
Author(s): |
Sadri Hassani |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences. |
Note: | Springer eBooks |
Contents: | Mathematical Preliminaries |
I Finite | |
Dimensional Vector Spaces | |
1 Vectors and Linear Maps | |
2 Algebras | |
3 Operator Algebra | |
4 Matrices | |
5 Spectral Decomposition | |
II Infinite | |
Dimensional Vector Spaces | |
6 Hilbert Spaces | |
7 Classical Orthogonal Polynomials | |
8 Fourier Analysis | |
III Complex Analysis | |
9 Complex Calculus | |
10 Calculus of Residues | |
11 Advanced Topics | |
IV Differential Equations | |
12 Separation of Variables in Spherical Coordinates | |
13 Second | |
Order Linear Differential Equations | |
14 Complex Analysis of SOLDEs | |
15 Integral Transforms and Differential Equ | |
ISBN: | 9783319011950 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2013-9783034806367:ONLINE Show nearby items on shelf |
Title: | Introduction to Mathematical Analysis [electronic resource] |
Author(s): |
Igor Kriz Ale Pultr |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, theLebesgue integral, vector calculus anddifferential equations. Af ter having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differentialgeometry and even functional analysis. Overall, this t ext provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Part 1. A Rigorous Approach to Advanced Calculus | |
1. Preliminaries | |
2. Metric and Topological Spaces I | |
3. Multivariable Differential Calculus | |
4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral | |
5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration | |
6. Systems of Ordinary Differential Equations | |
7. System of Linear Differential Equations | |
8. Line Integrals and Green's Theorem | |
Part 2. Analysis and Geometry | |
9. An Introduction to Complex Analysis | |
10. Metric and Top | |
ISBN: | 9783034806367 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Functions of complex variables , Differential Equations , Sequences (Mathematics) |
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Call number: | SPRINGER-2013-9781461479727:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis on Symmetric SpacesEuclidean Space, the Sphere, and the Poincar Upper Half-Plane [electronic resource] |
Author(s): |
Audrey Terras |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincar upper half plane. This book is intended for beginning graduate students inmathematics or researchers in phy sics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, andengineering. Many corrections, new topics, and updates have be en incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T.Sunada, Marie-France Vignras, Carolyn Gordon, and others on Mark Kac's question Can y ou hear the shape of a drum?, Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maasswaveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summationformula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon tr ansform, non-Euclidean geometry on the Poincar upper half plane H or unit disc andapplications to microwave engineering, fundamental domains in H for discrete groups , tessellations of H from such discrete group actions, automorphic forms, the Selberg tra ce formula and its applications in spectral theory as wellas number theory |
Note: | Springer eBooks |
Contents: | Chapter1 Flat Space. Fourier Analysis on R^m |
1.1 Distributions or Generalized Functions | |
1.2 Fourier Integrals | |
1.3 Fourier Series and the Poisson Summation Formula | |
1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions | |
1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyls Criterion for Uniform Distribution | |
Chapter2 A Compact Symmetric Space | |
The Sphere | |
2.1 Fourier Analysis on the Sphere | |
2.2 O(3) and R^3. The Radon Transform | |
Chapter 3 The Poincar Upper Half | |
Plane | |
3.1 Hyperbolic Geometry | |
3.2 Harmonic Analysis on H | |
3.3 Fundamental Domains for | |
ISBN: | 9781461479727 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Topological Groups , Harmonic analysis , Fourier analysis , Functions of complex variables , Functions, special |
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Call number: | SPRINGER-2013-9781461470984:ONLINE Show nearby items on shelf |
Title: | Overconvergence in Complex Approximation [electronic resource] |
Author(s): |
Sorin G Gal |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph deals with the quantitative overconvergence phenomenon in complex approximation by various operators. The book is divided into three chapters. First, the results for the Schurer-Faber operator, Beta operators offirst kind, Bernstein-Du rrmeyer-type operators and Lorentz operator are presented. The main focus is on results for several q-Bernstein kind of operators with q > 1, when the geometric order of approximation 1/q^n is obtained not onlyin complex compact disks but also in quaterni on compact disks and in other compact subsets of the complex plane. The focus then shifts to quantitative overconvergence and convolution overconvergence results for the complex potentialsgenerated by the Beta and Gamma Euler's functions. Finally quantita tive overconvergence results for the most classical orthogonal expansions (of Chebyshev, Legendre, Hermite, Laguerre and Gegenbauer kinds) attached tovector-valued functions are presented. Each chapter concludes with a notes and open problems section, thu s providing stimulation for further research. An extensive bibliography and index complete the text. This book is suitablefor researchers and graduate students working in complex approximation and its applications, mathematical analysis and numerical ana lysis |
Note: | Springer eBooks |
Contents: | Overconvergence in C of Some Bernstein |
Type Operators | |
Overconvergence and Convergence in C of Some IntegralConvolutions | |
Overconvergence in C of the Orthogonal Expansions | |
ISBN: | 9781461470984 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461469469:ONLINE Show nearby items on shelf |
Title: | Applications of q-Calculus in Operator Theory [electronic resource] |
Author(s): |
Ali Aral Vijay Gupta Ravi P Agarwal |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas suchas computer-aided geometric design, numericalanalysis, and solutions of dif ferential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. This monograph is an introduction to combining approximationtheory and q-Calculus with applications, by usingwell- known operators. The presentation is systematic and the authors include a brief summary of the notations and basicdefinitions ofq-calculus before delving into more advancedmaterial. Themany applications of q-calculus in the theory of approximation, espec ially onvariousoperators,which includes convergence of operators to functions in real and complex domain forms the gist of the book. This book issuitable for researchers andstudents in mathematics,physics andengineering,and forprofessionals who would enjo y exploring the host of mathematicaltechniques and ideas that are collected and discussedin thebook |
Note: | Springer eBooks |
Contents: | Introduction of q |
calculus | |
q | |
Discrete operators and their results | |
q | |
Integral operators | |
q | |
Bernstein type integral operators | |
q | |
Summation | |
integral operators | |
Statistical convergence of q | |
operators | |
q | |
Complex operators | |
ISBN: | 9781461469469 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables |
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Call number: | SPRINGER-2013-9781461459620:ONLINE Show nearby items on shelf |
Title: | Foundations of Abstract Analysis [electronic resource] |
Author(s): |
Jewgeni H Dshalalow |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presentedin a self-contained wa y suitable both for classroom use and for self-study. While this book carries the rigor of advancedmodern analysis texts, it elaborates the material in much greater details and therefore fills a gap betweenintroductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of thepotential overload of new words, definitions, and concepts, the book (in its u nique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded byinformal discussions and blueprints followed by thorough details andsupported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of thebook, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. P rerequisites include advanced calculus, linear algebra, complex variables, and calculus basedprobability |
Note: | Springer eBooks |
Contents: | Set |
Theoretic and Algebraic Preliminaries | |
Analysis of Metric Spaces | |
Elements of Point | |
Set Topology | |
Measurable Spaces and Measurable Functions | |
Measures | |
Integration in Abstract Spaces | |
Solutions to Selected Problems | |
Bibliography | |
List of Symbols | |
Index of Names and Terms | |
ISBN: | 9781461459620 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Numerical analysis |
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Call number: | SPRINGER-2013-9781461457251:ONLINE Show nearby items on shelf |
Title: | Hidden HarmonyGeometric Fantasies [electronic resource] : The Rise of Complex Function Theory |
Author(s): |
Umberto Bottazzini Jeremy Gray |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Hidden HarmonyGeometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted tocomplex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subjectCauchy, Riemann, and Weierstrassit looks at thecontributions of great mathematicians from dAlembert to Po incar, and Laplace to Weyl. Select chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric functiontheory, and the early years of complex function theory in several variables. Unique em phasis has been placed on the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages.This book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture o f the broad cultural and social context in which the main players lived and worked by paying attention to the rise ofmathematical schools and of contrasting national traditions. This work is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It is a major resource for professionalmathematicians as well as advanced undergraduate and graduate students and anyone studying complex function theory |
Note: | Springer eBooks |
Contents: | List of Figures |
Introduction | |
1. Elliptic Functions | |
2. From real to complex | |
3. Cauch | |
4. Elliptic integrals | |
5. Riemann | |
6. Weierstrass | |
7. Differential equations | |
8. Advanced topics | |
9. Several variables | |
10. Textbooks | |
ISBN: | 9781461457251 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Sources and Studies in the History of Mathematics and Physical Sciences |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Number theory |
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Call number: | SPRINGER-2013-9781461456117:ONLINE Show nearby items on shelf |
Title: | Derivatives of Inner Functions [electronic resource] |
Author(s): |
Javad Mashreghi |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Derivatives of Inner Functions was inspired by a conference held at the Fields Institute in 2011 entitled Blaschke Products and Their Applications. Inner functions form an important subclass of bounded analytic functions.Since they have unimodular bo undary values, they appear in many extremal problems of complex analysis. They have been extensively studied since the early twentieth century and the literature on this topic is vast. This book is devotedto a concise study of derivatives of inner functio ns and is confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. This self-contained monograph allowsresearchers to get acquainted with the essentials of inner functions, rendering this theory accessible to graduate students while providing the reader with rapid access to the frontiers of research in this field |
Note: | Springer eBooks |
ISBN: | 9781461456117 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fields Institute Monographs, 1069-5273 : v31 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461453413:ONLINE Show nearby items on shelf |
Title: | Blaschke Products and Their Applications [electronic resource] |
Author(s): |
Javad Mashreghi Emmanuel Fricain |
Date: | 2013 |
Publisher: | Boston, MA : Springer US : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Blaschke products have been researched for nearly a century. They haveshown to be important in several branches of mathematics through their boundary behaviour, dynamics, membership in different function spaces, and theasymptotic growth of various in tegral means of their derivatives. This volume presents a collection of survey and research articles thatexamine Blaschke products and several of their applications to fields such as approximationtheory, differential equations, dynamical systems, and har monic analysis. Additionally, it illustrates the historical roots of Blaschke products and highlights key research on this topic. The contributions, written by expertsfrom various fields of mathematical research, include several open problems. They will engage graduate students and researchers alike, bringing them to theforefront of research in the subject |
Note: | Springer eBooks |
ISBN: | 9781461453413 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fields Institute Communications, 1069-5265 : v65 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations , Functional analysis , Functions of complex variables |
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Call number: | SPRINGER-2013-9781461450580:ONLINE Show nearby items on shelf |
Title: | Uniform Spaces and Measures [electronic resource] |
Author(s): |
Jan Pachl |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Uniform Spaces and Measures addresses the need for an accessible and comprehensive exposition of the theory of uniform measures -- a need that became more critical when uniform measures recently reemerged in new results inabstract harmonic analysis. Until now, results about uniform measures have been scattered throughout many papers written by a number of authors, some unpublished, using a variety of definitions and notations. Uniform measures arefunctionals on the space of bounded uniformly continuo us functions on a uniform space. They are a common generalization of several classes of measures and measure-like functionals studied in topological measure theory, probabilitytheory, and abstract harmonic analysis. They offer a natural framework for resu lts about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups. Thisbook can serve as a reference for the theory of uniform measures. It includes a self-contained develop ment of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It also includes severalnew results, and presents diverse results from many sources organized in a logical whole. The content is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis, and containsa number of exercises with hints to solutions as well as several open problems with suggestions for further research |
Note: | Springer eBooks |
Contents: | Prerequisites |
1. Uniformities and Topologies | |
2. Induced Uniform Structures | |
3. Uniform Structures on Semigroups | |
4. Some Notable Classes of Uniform Spaces | |
5. Measures on Complete Metric Spaces | |
6. Uniform Measures | |
7. Uniform Measures as Measures | |
8. Instances of Uniform Measures | |
9. Direct Product and Convolution | |
10. Free Uniform Measures | |
11. Approximation of Probability Distributions | |
12. Measurable Functionals | |
Hints to Excercises | |
References | |
Notation Index | |
Author Index | |
Subject Index | |
ISBN: | 9781461450580 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fields Institute Monographs, 1069-5273 : v30 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Functions of complex variables |
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Call number: | SPRINGER-2013-9781441973238:ONLINE Show nearby items on shelf |
Title: | Complex Analysis [electronic resource] : In the Spirit of Lipman Bers |
Author(s): |
Rub E Rodrguez Irwin Kra Jane P Gilman |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas ofmathematics, including the theor y of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects inmathematics and to other sciences. Thus this material will also be of interest to computer scientists, physicists, and engineers. The book covers most, if not all, of the material contained in Lipman Berss courses on first yearcomplex analysis. In addition, topics of current interest, such as zeros of holom orphic functions and the connection between hyperbolic geometry and complex analysis, are explored. In addition to many new exercises, this second editionintroduces a variety of new and interesting topics. New features include a section on Bers's theorem on isomorphisms between rings of holomorphic functions on plane domains necessary and sufficient conditions for the existence of abounded analytic function on the disc with prescribed zeros sections on subharmonic functions and Perron's principle and a se ction on the ring of holomorphic functions on a plane domain. There are three new appendices: the first isa contribution by Ranjan Roy on the history of complex analysis, the second contains background material on exterior differential calculus, and the t hird appendix includes an alternate approach to the Cauchy theory |
Note: | Springer eBooks |
Contents: | Preface to Second Edition |
Preface to First Edition | |
Standard Notation and Commonly Used Symbols | |
1 The Fundamental Theorem in Complex Function Theory | |
2 Foundations | |
3 Power Series | |
4 The Cauchy Theory | |
A Fundamental Theorem | |
5 The Cauchy Theory | |
Key Consequences | |
6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions | |
7 Sequences and Series of Holomorphic Functions | |
8 Conformal Equivalence and Hyperbolic Geometry | |
9 Harmonic Functions | |
10 Zeros of Holomorphic Functions | |
Bibliographical Notes | |
Bibliography | |
Index | |
ISBN: | 9781441973238 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v245 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables |
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Call number: | SPRINGER-2012-9783834886613:ONLINE Show nearby items on shelf |
Title: | A Course in Complex Analysis [electronic resource] From Basic Results to Advanced Topics |
Author(s): |
Wolfgang Fischer Ingo Lieb |
Date: | 2012 |
Publisher: | Wiesbaden : Vieweg+Teubner Verlag |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe in the Anglo-Americansystem of university e ducation the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions(elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ) and a new feature in this context! to exhibiting basic facts in the theory of several complex variables. Part of the book is atranslation of the authors German text Einfhrung in die komplexe Analysis some material was added from the by now almost classical text Funktionentheorie written by the authors, and a few paragraphs were newlywritten for special use in a masters programme. Content Analysis in the complex plane - The fundamental theorems of complex a nalysis - Functions on the plane and on the sphere - Integral formulas, residues and applications -Non-elementary functions - Meromorphic functions of several variables - Holomorphic maps: Geometric aspects Readership Advanced undergraduates (bachelor stu dents) and beginning graduate students (master's programme) Lecturers inmathematics About the authors Professor Dr. Ingo Lieb, Department of Mathematics, University of Bonn Professor Dr. Wolfgang Fischer, Department of Mathematics, University of Bremen |
Note: | Springer eBooks |
ISBN: | 9783834886613 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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Call number: | SPRINGER-2012-9783642308987:ONLINE Show nearby items on shelf |
Title: | q -Fractional Calculus and Equations [electronic resource] |
Author(s): |
Mahmoud H Annaby Zeinab S Mansour |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9783642308987 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional equations , Functions of complex variables , Integral equations , Integral Transforms , Mathematical physics |
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Call number: | SPRINGER-2012-9783642298462:ONLINE Show nearby items on shelf |
Title: | Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces [electronic resource] : Topics from Differential Geometry and Geometric Analysis of Surfaces |
Author(s): |
Steffen Frhlich |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface geometry in higher-dimensionalEuclidean spaces, in p articular the differential equations of Gauss-Weingarten together with various integrability conditions and corresponding surface curvatures. It includes a chapter on curvature estimates for such surfaces, and,using results from potential theory and harmo nic analysis, it addresses geometric and analytic methods to establish the existence and regularity of Coulomb frames in their normal bundles, which arise as critical points for a functionalof total torsion |
Note: | Springer eBooks |
Contents: | Surface Geometry |
Elliptic Systems | |
Normal Coulomb Frames in R4 | |
Normal Coulomb Frames in Rn+2 | |
ISBN: | 9783642298462 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2053 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2012-9783642293023:ONLINE Show nearby items on shelf |
Title: | Modular Forms with Integral and Half-Integral Weights [electronic resource] |
Author(s): |
Xueli Wang Dingyi Pei |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Modular Forms with Integral and Half-Integral Weights focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series.It is a fundamental proble m to construct a basis of the orthogonal complement of the space of cusp forms as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that theconclusion holds true for weight 3/2 by explicit ly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. Thebook provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers andpractitioners in modular forms of mathematics. Dr. Xueli Wang is a Professor at South China No rmal University, China. Dingyi Pei is a Professor at Guangzhou University, China |
Note: | Springer eBooks |
Contents: | Theta Functions and Their Transformation Formulae |
Eisenstein Series | |
The Modular Group and Its Subgroups | |
Modular Forms with Integral Weight or Half | |
integral Weight | |
Operators on the Space of Modular Forms | |
New Forms and Old Forms | |
Construction of Eisenstein Series | |
Weil Representation and Shimura Lifting | |
Trace Formula | |
Integers Represented by Positive Definite Quadratic Forms | |
ISBN: | 9783642293023 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Functions of complex variables , Number theory |
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Call number: | SPRINGER-2012-9783642256349:ONLINE Show nearby items on shelf |
Title: | Extremal Polynomials and Riemann Surfaces [electronic resource] |
Author(s): |
Andrei Bogatyrev |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The problems of conditional optimization of the uniform (or C-) norm for polynomials and rational functions arise in various branches of science and technology. Their numerical solution is notoriously difficult in case of highdegree functions. The bo ok develops the classical Chebyshev's approach which gives analytical representation for the solution in terms of Riemann surfaces. The techniques born in the remote (at the first glance) branches of mathematicssuch as complex analysis, Riemann surfaces a nd Teichmller theory, foliations, braids, topology are applied to approximation problems. The key feature of this book is the usage of beautiful ideas of contemporary mathematics for thesolution of applied problems and their effective numerical realizatio n. This is one of the few books where the computational aspects of the higher genus Riemann surfaces are illuminated. Effective work with the moduli spaces ofalgebraic curves provides wide opportunities for numerical experiments in mathematics and theoret ical physics |
Note: | Springer eBooks |
Contents: | 1 Least deviation problems |
2 Chebyshev representation of polynomials | |
3 Representations for the moduli space | |
4 Cell decomposition of the moduli space | |
5 Abels equations | |
6 Computations in moduli spaces | |
7 The problem of the optimal stability polynomial | |
Conclusion | |
References | |
ISBN: | 9783642256349 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Global analysis , Numerical analysis , Engineering mathematics |
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Call number: | SPRINGER-2012-9783642256202:ONLINE Show nearby items on shelf |
Title: | A Theory of Branched Minimal Surfaces [electronic resource] |
Author(s): |
Anthony Tromba |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not i.e. does its derivative have maximal rank everywhere. The purpose of this monographis to present an elemen tary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energyas opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in theCalculus of Variations, where normally only the second derivativ e or variation is calculated. The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in eithermanifolds or complex analysis. Thus this monograph requires only the most basic knowled ge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education |
Note: | Springer eBooks |
Contents: | 1.Introduction |
2.Higher order Derivatives of Dirichlets' Energy | |
3.Very Special Case The Theorem for n + 1 Even and m + 1 Odd | |
4.The First Main Theorem Non | |
Exceptional Branch Points | |
5.The Second Main Theorem: Exceptional Branch Points The Condition k > l | |
6.Exceptional Branch Points Without The Condition k > l | |
7.New Brief Proofs of the Gulliver | |
Osserman | |
Royden Theorem | |
8.Boundary Branch Points | |
Scholia | |
Appendix | |
Bibliography | |
ISBN: | 9783642256202 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Global analysis , Sequences (Mathematics) , Global differential geometry |
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Call number: | SPRINGER-2012-9783034804288:ONLINE Show nearby items on shelf |
Title: | Interpolation, Schur Functions and Moment Problems II [electronic resource] |
Author(s): |
Daniel Alpay Bernd Kirstein |
Date: | 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parametersequences. Schur ana lysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricialgeneralizations. These problems include interpolation a nd moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics relatedto matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number ofrecent developments in orthogonal rational matrix functions, matrix-valued Carathodory functions a nd maximal weight solutions for particular matricial moment problems on the unit circle |
Note: | Springer eBooks |
ISBN: | 9783034804288 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v226 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Integral Transforms , Operator theory |
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Call number: | SPRINGER-2012-9783034804172:ONLINE Show nearby items on shelf |
Title: | Advances in Applied Analysis [electronic resource] |
Author(s): |
Sergei V Rogosin Anna A Koroleva |
Date: | 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book contains survey papers based on the lectures presented at the 3rd International Winter School Modern Problems of Mathematics and Mechanics held in January 2010 at the Belarusian State University, Minsk. Theselectures are devoted to differen t problems of modern analysis and its applications. An extended presentation of modern problems of applied analysis will enable the reader to get familiar with new approaches of mostly interdisciplinarycharacter. The results discussed are application orie nted and present new insight into applied problems of growing importance such as applications to composite materials, anomalous diffusion, and fluid dynamics |
Note: | Springer eBooks |
Contents: | Introduction |
Kisil, Vladimir V.: Erlangen Program at Large: Brief Outline | |
Laurincikas, A.: The Riemann zeta | |
function: approximation of analytic functions | |
Luchko, Yury: Anomalous diffusion: models, their analysis, and interpretation | |
Mityushev, Vladimir, V.: R | |
linear and Riemann | |
Hilbert problems for multiply connected domains | |
Plaksa, S. A.: Commutative algebras associated with classic equations of mathematical physics | |
Rogosin, Sergei V.: 2D Free Boundary Value Problems | |
ISBN: | 9783034804172 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Differential equations, partial , Number theory |
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Call number: | SPRINGER-2012-9783034804110:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods in Systems, Optimization, and Control [electronic resource] : Festschrift in Honor of J. William Helton |
Author(s): |
Harry Dym Mauricio C Oliveira Mihai Putinar |
Date: | 2012 |
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 Bill Helton on the occasion of his sixty-fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization andcontrol, and 19 techn ical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty-oddyears. These include interpolation, Szeg limi t theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful tograduate students in mathematics and engineering, as well as to facult y and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure andapplied mathematicsand engineering, and as a source book for seminars |
Note: | Springer eBooks |
Contents: | Preface |
Inroduction (an overview of the contents of the book, from the perspective of Helton's landmark contributions) | |
Biographical Note and List of Publications of J.W. Helton | |
Bounded Analytic Interpolation and H | |
infinity Control | |
Linear Matrix Inequalities and Matrix Convexity | |
Optimization and Realization in the Free * | |
algebra | |
Automatic Verification of Matrix Inequalities | |
Non | |
commutative Algebraic Geometry | |
Non | |
Commutative Differential Geometry and Probability | |
Modern Trends in Robust Control | |
Challenges of Mathematical Biology | |
Mathematical Programming and Comput | |
ISBN: | 9783034804110 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v222 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Functions of complex variables , Operator theory |
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Call number: | SPRINGER-2012-9783034803465:ONLINE Show nearby items on shelf |
Title: | Recent Progress in Operator Theory and Its Applications [electronic resource] |
Author(s): |
Joseph A Ball Ral E Curto Sergei M Grudsky J. William Helton Ral Quiroga-Barranco Nikolai L Vasilevski |
Date: | 2012 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume contains twenty-one solicited articles by speakers at the IWOTA 2009 workshop, ranging from expository surveys to original research papers, each carefully refereed.The contributions reflect recent developments inoperator theory and its ap plications. Consistent with the topics of recent IWOTA meetings, IWOTA 2009 was designed as a comprehensive, inclusive conference covering all aspects of theoretical and applied operator theory, ranging fromclassical analysis, differential and integral eq uations, complex and harmonic analysis to mathematical physics, mathematical systems and control theory, signal processing and numerical analysis. The conference brought togetherinternational experts for a week-long stay at Hotel Real de Minas, in an atmo sphere conducive to fruitful, professional interactions. These proceedings reflect the high quality of the papers presented at the conference |
Note: | Springer eBooks |
ISBN: | 9783034803465 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v220 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2012-9783034801805:ONLINE Show nearby items on shelf |
Title: | Visual Complex Functions [electronic resource] : An Introduction with Phase Portraits |
Author(s): |
Elias Wegert |
Date: | 2012 |
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 a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations so-called phase portraits which visualize functions as images ontheir domains. Reading Visua l Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course oncomplex analysis. With separate chapters on variou s construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline,running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endowindividual faces to analytic functions. Phase portraits enhance the intuitive understanding of conc epts in complex analysis and are expected to be useful tools for anybody working with special functions even experienced researchersmay be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion t o other texts or as a reference work for advanced readers who wish to know more about phase portraits |
Note: | Springer eBooks |
Contents: | Preface |
1. Getting Acquainted | |
2. Complex Functions | |
3. Analytic Functions | |
4. Complex Calculus | |
5. Construction Principles | |
6. Conformal Mappings | |
7. Riemann Surfaces | |
ISBN: | 9783034801805 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Functions, special |
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Call number: | SPRINGER-2012-9781461443407:ONLINE Show nearby items on shelf |
Title: | Introduction to Piecewise Differentiable Equations [electronic resource] |
Author(s): |
Stefan Scholtes |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This briefprovidesanelementaryintroduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study ofthis theory.The presentation is th en developedusingtwo basic tools for the analysis of piecewise differentiable functions:the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory ofpiecewise affine functions as the combinatorial tool for the st udy of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piecewise differentiable equations. ThisIntroduction to Piecewise Differentiable Equations will serve graduate students and rese archers alike. The reader is assumed to be familiar with basic mathematical analysis and to have some familiarity with polyhedral theory |
Note: | Springer eBooks |
ISBN: | 9781461443407 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Optimization, 2190-8354 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functions of complex variables , Mathematical optimization |
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Call number: | SPRINGER-2012-9781461432265:ONLINE Show nearby items on shelf |
Title: | Pyomo Optimization Modeling in Python [electronic resource] |
Author(s): |
William E Hart Carl Laird Jean-Paul Watson David L Woodruff |
Date: | 2012 |
Publisher: | Boston, MA : Springer US |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides a complete and comprehensive guide to Pyomo(Python Optimization Modeling Objects) for beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, andpractitioners. Modeling is a fundamental process in many aspects of scientific research, engineering, and business. This text beautifully illustrates the breadth of the modeling capabilities that are supported by this new software andits handling of complex real-world applications . Pyomo is an open source software package for formulating and solving large-scale optimization problems. The software extends the modeling approach supported by modern AML (AlgebraicModeling Language) tools.Pyomo is a flexible, extensible, and portable AML that is embedded in Python, a full-featured scripting language.Python is a powerful and dynamic programming language that has a very clear, readable syntaxand intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parame ters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can beused from a command-line interface and within Python's interactive command environment, which makes it easy to create P yomo models, apply a variety of optimizers, and examine solutions. The text begins with a tutorial on simplelinear and integer programming models. Information needed to install and get started with the software is also provided. A detailed reference of P yomo's modeling components is illustrated with extensive examples, including a discussionof how to load data from sources like spreadsheets and databases. The final chapters cover advanced topics such as nonlinear models, stochastic models, and scripting examples |
Note: | Springer eBooks |
Contents: | Preface |
1. Introduction | |
2. Pyomo Modeling Strategies | |
3. Model Components: Variables, Objectives and Constraints | |
4. Model Components: Sets and Parameters | |
5. Mischellaneous Model Components and Utility Functions | |
6. Initializing Abstract Models with Data Command Files | |
7. The Pyomo Command | |
Line Interface | |
8. Nonlinear Programming with Pyomo | |
9. Stochastic Programming Extensions | |
10. Scripting and Algorithm Development | |
A. Installing Coopr | |
B. A Brief Python Tutorial | |
C. Pyomo and Coopr: The Bigger Picture | |
Index | |
ISBN: | 9781461432265 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Optimization and Its Applications, 1931-6828 : v67 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Computer simulation , Computer science Mathematics , Computer software , Mathematical optimization |
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Call number: | SPRINGER-2012-9781461431916:ONLINE Show nearby items on shelf |
Title: | The Beltrami Equation [electronic resource] A Geometric Approach |
Author(s): |
Vladimir Gutlyanskii Vladimir Ryazanov Uri Srebro Eduard Yakubov |
Date: | 2012 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The Beltrami Equation: A Geometric Approach will be particularly useful to many specialists in modern geometric analysis, quasiconformal mappings and extensions, beginning researchers, and graduate students with a yearsbackground in complex variables . This book covers the state-of-the art in the ongoing study of the Beltrami equation, the classical equation that has been studied for more than 100 years. Along with its rich history, the Beltramiequation plays a significant role in geometry, analysis, and physics. The most important feature of this workconcerns the unified geometric approach taken based on the modulus method that can be effectively applied to solving manyproblems in mathematical physics. Beautiful examples illustrate the relationship between mappings with bounded oscillation and those with finite oscillations. Written by authors that are well-known specialists in this field, thismonograph presents recent developments in the theory of Beltrami equations, studying a variety of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates, and boundarybehaviorof solutions to the Beltrami equations. It contains new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be notonly sufficient but also necessary |
Note: | Springer eBooks |
Contents: | 1. Introduction |
2. Preliminaries | |
3. The Classical Beltrami Equation |||| < 1 | |
4. The Degenerate Case | |
5. BMO | |
and FMO | |
Quasiconformal Mappings | |
6. Ring Q | |
Homeomorphisms at Boundary Points | |
7. Strong Ring Solutions of Beltrami Equations | |
8. On the Dirichlet Problem for Beltrami Equations | |
9. On the Beltrami Equations with Two Characteristics | |
10. Alternating Beltrami Equation | |
References | |
Index | |
ISBN: | 9781461431916 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Developments in Mathematics, 1389-2177 : v26 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2012-9781447140085:ONLINE Show nearby items on shelf |
Title: | Complex Analysis and Differential Equations [electronic resource] |
Author(s): |
Luis Barreira Claudia Valls |
Date: | 2012 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations.The text is divided i nto two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book,some emphasis is given to the application of c omplex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variablelevels of difficulty. Tailored to any course giving the first introduc tion to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, thelarge number of examples, worked out problems and exercises makes this the ideal book for i ndependent study |
Note: | Springer eBooks |
Contents: | Part 1 Complex Analysis |
Basic Notions | |
Holomorphic Functions | |
Sequences and Series | |
Analytic Functions | |
Part 2 Differential Equations | |
Ordinary Differential Equations | |
Solving Differential Equations | |
Fourier Series | |
Partial Differential Equations | |
ISBN: | 9781447140085 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functions of complex variables , Differential Equations , Differential equations, partial , Sequences (Mathematics) |
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