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Call number: | 9783319527420:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis, Partial Differential Equations and Applications In Honor of Richard L. Wheeden |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (XXIV, 301 p p.) |
ISBN: | 9783319527420 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Harmonic analysis , Partial differential equations , Numerical analysis , Mathematics , Partial Differential Equations , Abstract Harmonic Analysis , Numerical Analysis |
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Call number: | SPRINGER-2016-9783319397801:ONLINE Show nearby items on shelf |
Title: | Extensions of Positive Definite Functions Applications and Their Harmonic Analysis |
Author(s): |
Palle Jorgensen |
Date: | 2016 |
Size: | 1 online resource (9 p.) |
Note: | 10.1007/978-3-319-39780-1 |
ISBN: | 9783319397801 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2160 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Fourier analysis , Functional analysis , Probabilities , Mathematical physics , Mathematics , Abstract Harmonic Analysis , Topological Groups, Lie Groups , Fourier Analysis , Functional Analysis , Mathematical Physics , Probability Theory and Stochastic Processes |
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Call number: | SPRINGER-2016-9783319300344:ONLINE Show nearby items on shelf |
Title: | An Introductory Course in Lebesgue Spaces |
Author(s): |
Rene Erlin Castillo |
Date: | 2016 |
Size: | 1 online resource (461 p.) |
Note: | 10.1007/978-3-319-30034-4 |
Contents: | Convex Functions and Inequalities -- Lebesgue Sequence Spaces -- Lebesgue Spaces -- Distribution Function and Non-Increasing Rearrangement -- Weak Lebesgue Spaces -- Lorentz Spaces -- Non-Standard Lebesgue Spaces -- Interpolation of Operators -- Ma ximal Operator -- Integral Operators -- Convolution and Potentials -- Appendices |
ISBN: | 9783319300344 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Mathematics , Abstract Harmonic Analysis , Functional Analysis |
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Call number: | SPRINGER-2016-9783319295589:ONLINE Show nearby items on shelf |
Title: | Quantization on Nilpotent Lie Groups |
Author(s): |
Veronique Fischer |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (557 p.) |
Note: | 10.1007/978-3-319-29558-9 |
Contents: | Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-d ifferential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index |
ISBN: | 9783319295589 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics: 314 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Functional analysis , Mathematical physics , Mathematics , Topological Groups, Lie Groups , Abstract Harmonic Analysis , Functional Analysis , Mathematical Physics |
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Call number: | SPRINGER-2016-9783319278735:ONLINE Show nearby items on shelf |
Title: | New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing, and Multifractal Analysis |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (19 p.) |
Note: | 10.1007/978-3-319-27873-5 |
Contents: | Multifractal Analysis of Cantor-like Measures -- Multifractal Analysis and Wavelets -- An Introduction to Mandelbrot Cascades -- Lebesgue-type Inequalities for Greedy Approximation -- Results on Non-linear Approximation for Wavelet Bases in Weighte d Function Spaces -- Consequences of the Marcus/Spielman/Srivastava Solution of the Kadison-Singer Problem -- Model Sets and New Versions pf Shannon Sampling Theorem -- Stylometry and Mathematical Study of Authorship -- Thoughts on Numerical and Conceptua l Harmonic Analysis |
ISBN: | 9783319278735 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Measure theory , Computer science , Computer mathematics , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Signal, Image and Speech Processing , Measure and Integration , Mathematical Applications in Computer Science |
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Call number: | SPRINGER-2016-9783319276984:ONLINE Show nearby items on shelf |
Title: | Moving Interfaces and Quasilinear Parabolic Evolution Equations |
Author(s): |
Jan Prüss |
Date: | 2016 |
Size: | 1 online resource (609 p.) |
Note: | 10.1007/978-3-319-27698-4 |
Contents: | Preface -- Basic Notations -- General References -- Part I Background -- 1Problems and Strategies -- 2.Tools from Differential Geometry -- Part II Abstract Theory -- 3Operator Theory and Semigroups -- 4.Vector-Valued Harmonic Analysis -- 5.Quasilin ear Parabolic Evolution Equations -- Part III Linear Theory -- 6.Elliptic and Parabolic Problems -- 7.Generalized Stokes Problems -- 8.Two-Phase Stokes Problems -- Part IV Nonlinear Problems -- 9.Local Well-Posedness and Regularity -- 10.Linear Stability of Equilibria -- 11.Qualitative Behaviour of the Semiows -- 12.Further Parabolic Evolution Problems -- Biographical Comments -- Outlook and Future Challenges -- References -- List of Figures -- List of Symbols -- Subject Index |
ISBN: | 9783319276984 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Monographs in Mathematics: 105 |
Keywords: | Mathematics , Functional analysis , Partial differential equations , Physics , Mathematics , Partial Differential Equations , Mathematical Methods in Physics , Functional Analysis |
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Call number: | SPRINGER-2016-9783319276663:ONLINE Show nearby items on shelf |
Title: | The Spectrum of Hyperbolic Surfaces |
Author(s): |
Nicolas Bergeron |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (370 p.) |
Note: | 10.1007/978-3-319-27666-3 |
Contents: | Preface -- Introduction -- Arithmetic Hyperbolic Surfaces -- Spectral Decomposition -- Maass Forms -- The Trace Formula -- Multiplicity of lambda1 and the Selberg Conjecture -- L-Functions and the Selberg Conjecture -- Jacquet-Langlands Corresponde nce -- Arithmetic Quantum Unique Ergodicity -- Appendices -- References -- Index of notation -- Index -- Index of names |
ISBN: | 9783319276663 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Dynamics , Ergodic theory , Hyperbolic geometry , Mathematics , Hyperbolic Geometry , Abstract Harmonic Analysis , Dynamical Systems and Ergodic Theory |
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Call number: | SPRINGER-2016-9783319274669:ONLINE Show nearby items on shelf |
Title: | Methods of Fourier Analysis and Approximation Theory |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (258 p.) |
Note: | 10.1007/978-3-319-27466-9 |
Contents: | 1. Introduction -- 2. Fourier analysis -- 2.1. Parseval frames -- 2.2. Hyperbolic Hardy classes and logarithmic Bloch spaces -- 2.3. Logan's and Bohman's extremal problems -- 2.4. Weighted estimates for the Hilbert transform -- 2.5. Q-Measures and uniqueness sets for Haar series -- 2.6. O-diagonal estimates for Calderón-Zygmund operators -- 3. Function spaces of radial functions -- 3.1. Potential spaces of radial functions -- 3.2. On Leray's formula -- 4. Approximation theory -- 4.1. Approximation order of Besov classes -- 4.2. Ulyanov inequalities for moduli of smoothness -- 4.3. Approximation order of Besov classes -- 5. Optimization theory and related topics -- 5.1. The Laplace-Borel transform -- 5.2. Optimization control problems -- 2 Michael Ruzhansky and Sergey Tikhonov.-5.3. Optimization control problems for parabolic equation -- 5.4. Numerical modeling of the linear filtration -- References. |
ISBN: | 9783319274669 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Numerical analysis , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Numerical Analysis |
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Call number: | SPRINGER-2016-9783319256139:ONLINE Show nearby items on shelf |
Title: | An Introduction to Frames and Riesz Bases |
Author(s): |
Ole Christensen |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (5 p.) |
Note: | 10.1007/978-3-319-25613-9 |
Contents: | Frames in Finite-dimensional Inner Product Spaces -- Infinite-dimensional Vector Spaces and Sequences -- Bases -- Bases and their Limitations -- Frames in Hilbert Spaces -- Tight Frames and Dual Frame Pairs -- Frames versus Riesz Bases -- Selected Topics in Frame Theory -- Frames of Translates -- Shift-Invariant Systems in l2(R) -- Gabor Frames in L2(R) -- Gabor Frames and Duality -- Selected Topics on Gabor Frames -- Gabor Frames in ℓ2(Z),L2(0,L),CL -- General Wavelet Frames in L2(R) -- Dyadic W avelet Frames for L2(R) -- Frame Multiresolution Analysis -- Wavelet Frames via Extension Principles -- Selected Topics on Wavelet Frames -- Generalized Shift-Invariant Systems in L2(Rd) -- Frames on Locally Compact Abelian Groups -- Perturbation of Frame s -- Approximation of the Inverse Frame Operator -- Expansions in Banach Spaces. Appendix |
ISBN: | 9783319256139 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Operator theory , Mathematics , Functional Analysis , Abstract Harmonic Analysis , Operator Theory , Signal, Image and Speech Processing |
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Call number: | SPRINGER-2016-9781493934089:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations |
Author(s): |
Audrey Terras |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (21 p.) |
Note: | 10.1007/978-1-4939-3408-9 |
ISBN: | 9781493934089 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Applied mathematics , Engineering mathematics , Geometry , Number theory , Combinatorics , Statistics , Mathematics , Abstract Harmonic Analysis , Number Theory , Geometry , Combinatorics , Applications of Mathematics , Statistical Theory and Methods |
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Call number: | SPRINGER-2014-9783034806947:ONLINE Show nearby items on shelf |
Title: | A Course on Integration Theory [electronic resource] : including more than 150 exercises with detailed answers |
Author(s): |
Nicolas Lerner |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathodory Theorem. It also includes some elementary properties ofHausdorff measures as we ll as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change-of-variables formulas as well as the constructionand study of classical Cantor sets are treate d in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality, are proven. Further topics include the Radon-Nikodym theorem, notions ofharmonic analysis, classical inequalities and interpolation theore ms including Marcinkiewicz's theorem, and the definition of Lebesgue points and the Lebesgue differentiation theorem. Each chapter ends with a large number of exercisesand detailed solutions. A comprehensive appendix provides the reader with various eleme nts of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. It also provides more advancedmaterial such as some basic properties of cardinals and ordinals which are useful for the study of measurabi lity |
Contents: | 1 Introduction |
2 General theory of integration | |
3 Construction of the Lebesgue measure on R^d | |
4 Spaces of integrable functions | |
5 Integration on a product space | |
6 Diffeomorphisms of open subsets of R^d and integration | |
7 Convolution | |
8 Complex measures | |
9 Harmonic analysis | |
10 Classical inequalities | |
ISBN: | 9783034806947 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2013-9783319008493:ONLINE Show nearby items on shelf |
Title: | Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces [electronic resource] |
Author(s): |
Toka Diagana |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as wellas their recent gene ralizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standardreferences that currently exist on those ne w classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basicintroductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers inmathematics as well as in engineering, in physics, and related areas. Further, some parts o f the book may be used for various graduate and undergraduate courses |
Note: | Springer eBooks |
Contents: | 1. Metric, Banach, and Hilbert Spaces |
2. Linear Operators on Banach Spaces | |
3. Almost Periodic Functions | |
4. Almost Automorphic Functions | |
5. Pseudo | |
Almost Periodic Functions | |
6. Pseudo | |
Almost Automorphic Functions | |
7. Existence Results for Some Second | |
Order Differential Equations | |
8. Existence Results to Some Integrodifferential Equations | |
9. Existence of C(m) | |
Pseudo | |
Almost Automorphic Solutions | |
10. Pseudo | |
Almost Periodic Solutions to Some Third | |
Order Differential Equations | |
11. Pseudo | |
Almost Automorphic Solutions to Some Sobolev | |
Type Equations | |
12. Stability Results f | |
ISBN: | 9783319008493 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Operator theory , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034805483:ONLINE Show nearby items on shelf |
Title: | Variable Lebesgue Spaces [electronic resource] : Foundations and Harmonic Analysis |
Author(s): |
David V Cruz-Uribe Alberto Fiorenza |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They wereintroduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, andfor their applications to problems in physics and ima ge processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-onapproach that makes clear the similarities and differences between the vari able and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewoodmaximal operator is completely developed, and the connections between variable Lebesguespaces and t he weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Rieszpotentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolatio n from the theory of weighted norm inequalities. The final chapter applies the results from previouschapters to prove basic results about variable Sobolev spaces |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Structure of Variable Lebesgue Spaces | |
3 The Hardy | |
Littlewood Maximal Operator | |
4 Beyond Log | |
Hlder Continuity | |
5 Extrapolation in the Variable Lebesgue Spaces | |
6 Basic Properties of Variable Sobolev Spaces | |
Appendix: Open Problems | |
Bibliography | |
Symbol Index | |
Author Index | |
Subject Index. | |
ISBN: | 9783034805483 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Global analysis |
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Call number: | SPRINGER-2013-9781461482086:ONLINE Show nearby items on shelf |
Title: | Distributions, Partial Differential Equations, and Harmonic Analysis [electronic resource] |
Author(s): |
Dorina Mitrea |
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 aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. Thebook is written in a for mat suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to coverall intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have beencarefully chosen to amplify the effect, and substantiate the power and scop e, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematicalinterests will find this book to be a useful resource and complete self-study guide. Throughout, a spe cial effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance tosee the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed too ls (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonicanalysis, at the earliest opportunity |
Note: | Springer eBooks |
Contents: | Introduction |
Summary of Topological and Functional Analysis Results | |
Weak Derivatives | |
The Space D0() of Distributions | |
The Fourier Transform | |
The Space of Tempered Distributions | |
Fundamental Solution | |
The Laplace Operator | |
The Heat Operator | |
The Wave Operator | |
The Lame Operator | |
Fundamental Solutions for Other Operators | |
Hypoelliptic operators | |
Sobolev spaces | |
Appendix | |
References. | |
ISBN: | 9781461482086 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Differential equations, partial , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9781461471936:ONLINE Show nearby items on shelf |
Title: | Lie Groups: Structure, Actions, and Representations [electronic resource] : In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday |
Author(s): |
Alan Huckleberry Ivan Penkov Gregg Zuckerman |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profoundcontributions to mathematics. D ue to Professor Wolfs broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods areemployed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representationspaces are discussed. Contributions in the area of representation theory involve numero us viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V . Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Kornyi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. rsted |
Note: | Springer eBooks |
Contents: | Preface |
Real group orbits on flag manifolds | |
Complex connections with trivial holonomy | |
Indefinite harmonic theory and harmonic spinors | |
Twistor theory and the harmonic hull | |
Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets | |
Propagation of the multiplicity | |
freeness property for holomorphic vector bundles | |
Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains | |
Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf | |
Weakly harmonic Maa forms and the princi | |
ISBN: | 9781461471936 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v306 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Functional analysis |
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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-2013-9781461445654:ONLINE Show nearby items on shelf |
Title: | Recent Advances in Harmonic Analysis and Applications [electronic resource] : In Honor of Konstantin Oskolkov |
Author(s): |
Dmitriy Bilyk Laura De Carli Alexander Petukhov Alexander M Stokolos Brett D Wick |
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: | Recent Advances in Harmonic Analysis and Applications is dedicated to the 65th birthday ofKonstantin Oskolkov and features contributions from analysts around the world. The volume contains expository articles by leadingexperts in their fields, as we ll asselected high quality research papers that explorenew results and trends in classical and computational harmonic analysis, approximation theory, combinatorics, convex analysis, differentialequations, functional analysis, Fourier analysis, graph theor y, orthogonal polynomials, special functions, and trigonometric series. Numerous articles in the volume emphasize remarkable connections between harmonic analysis andother seemingly unrelated areas of mathematics, such as the interaction between abstract problems in additive number theory, Fourier analysis, and experimentally discovered optical phenomena in physics. Survey and research articlesprovide an up-to-date account of various vital directions of modern analysis and will in particularbeof interest to young researchers who are just starting their career. This book will also be useful to experts in analysis,discrete mathematics, physics, signal processing, and other areas of science |
Note: | Springer eBooks |
ISBN: | 9781461445654 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v25 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Harmonic analysis , Differential equations, partial , Algorithms , Number theory |
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Call number: | SPRINGER-2011-9780817646875:ONLINE Show nearby items on shelf |
Title: | A Basis Theory Primer [electronic resource] Expanded Edition |
Author(s): |
Christopher Heil |
Date: | 2011 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frameexpansions and its use i n both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. * Part I develops thefunctional analysis that underlies most of the concepts presented in the later parts of the text. * Part II presents the abstract theory of bases and frames in Banach and Hilbert spaces, including the classical topics of convergence,Schauder bases, biorthogonal systems, and unconditional bases, follo wed by the more recent topics of Riesz bases and frames in Hilbert spaces. * Part III relates bases and frames to applied harmonic analysis, including sampling theory,Gabor analysis, and wavelet theory. * Part IV deals with classical harmonic analysis and Fourier series, emphasizing the role played by bases, which is a different viewpoint from that taken in most discussions of Fourier series. Keyfeatures: * Self-contained presentation with clear proofs accessible to graduate students, pure and applied mat hematicians, and engineers interested in the mathematical underpinnings of applications. * Extensive exercises complementthe text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses hints for selected exerc ises are included at the end of the book. * A separate solutions manual is available for instructorsupon request at: www.birkhauser-science.com/978-0-8176-4686-8/. * No other text develops the ties between classical basis theory and its modern uses in app lied harmonic analysis. A Basis Theory Primer is suitable for independent studyor as the basis for a graduate-level course. Instructors have several options for building a course around the text depend |
Note: | Springer eBooks |
Contents: | ANHA Series Preface |
Preface | |
General Notation | |
Part I. A Primer on Functional Analysis | |
Banach Spaces and Operator Theory | |
Functional Analysis | |
Part II. Bases and Frames | |
Unconditional Convergence of Series in Banach and Hilbert Spaces | |
Bases in Banach Spaces | |
Biorthogonality, Minimality, and More About Bases | |
Unconditional Bases in Banach Spaces | |
Bessel Sequences and Bases in Hilbert Spaces | |
Frames in Hilbert Spaces | |
Part III. Bases and Frames in Applied Harmonic Analysis | |
The Fourier Transform on the Real Line | |
Sampling, Weighted Exponentials, and Translations | |
ISBN: | 9780817646875 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Functional analysis , Engineering mathematics |
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Call number: | SPRINGER-2010-9780387709147:ONLINE Show nearby items on shelf |
Title: | Functional Analysis, Sobolev Spaces and Partial Differential Equations [electronic resource] |
Author(s): |
Haim Brezis |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct worlds, functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have agood background in real analys is. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there aremany books on functional analysis and many on PDEs , this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research.This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of the important Analyse Fonctionnelle (1983). Since the French book was firstpublished, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chin ese. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operatortheory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specifi c differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theoryof PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs wh ich arise, for example, in differential geometry, harmonic analysis, engineering, mechanics,physics etc. and belong in the toolbox of any graduate student studying analysis |
Note: | Springer eBooks |
Contents: | Preface |
1. The HahnBanach Theorems. Introduction to the Theory of Conjugate Convex Functions | |
2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators | |
3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity | |
4. L^p Spaces | |
5. Hilbert Spaces | |
6. Compact Operators. Spectral Decomposition of Self | |
Adjoint Compact Operators | |
7. The HilleYosida Theorem | |
8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension | |
9. Sobolev Spaces and the Vari | |
ISBN: | 9780387709147 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Differential equations, partial |
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Call number: | SPRINGER-2009-9783764389949:ONLINE Show nearby items on shelf |
Title: | Observation and Control for Operator Semigroups [electronic resource] |
Author(s): |
Marius Tucsnak George Weiss |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book studies observation and control operators for linear systems where the free evolution of the state can be described by an operator semigroup on a Hilbert space. The emphasis is on well-posedness, observability andcontrollability properties. The abstract results are supported by a large number of examples coming mostly from partial differential equations. These examples are worked out in detail. This book is meant to be an elementaryintroduction in this theory. The first meaning of elementar y'' is that the text is aimed to be accessible to any reader familiar with linear algebra, calculus, the basics of Hilbert spaces and differential equations. We introduceeverything needed on operator semigroups and most of the background used is summarize d in the Appendices, often with proofs. The second meaning of elementary'' is that we only cover results for which we can provide complete proofs.In our bibliographic comments we mention some of the more advanced results, for example those based on microl ocal analysis |
Note: | Springer eBooks |
Contents: | Preface |
1. Finite | |
dimensional Systems | |
2. Operator Semigroups | |
3. Semigroups of Contractions | |
4. Control and Observation Operators | |
5. Observability | |
6. Observation for the Wave Equation | |
7. Non | |
harmonic Fourier Series and Exact Observability | |
8. Observability for Parabolic Equations | |
9. Boundary Control Systems | |
10. Controllability | |
Appendices | |
References | |
ISBN: | 9783764389949 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Birkhuser Advanced Texts / Basler Lehrbcher |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Differential equations, partial , Systems theory |
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Call number: | SPRINGER-2009-9780387854694:ONLINE Show nearby items on shelf |
Title: | Principles of Harmonic Analysis [electronic resource] |
Author(s): |
Anton Deitmar Siegfried Echterhoff |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The present book is intended as a text for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up to Anton Deitmer's previous book, A First Course in Harmonic Analysis, orindependently, if the studen ts already have a modest knowledge of Fourier Analysis. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not provedin A First Course in Harmonic Analysis. Using Po ntryagin duality, the authors also obtain various structure theorems for locally compact abelian groups. The book then proceeds with Harmonic Analysis on non-abelian groups and itsapplications to theory in number theory and the theory of wavelets. Knowled ge of set theoretic topology, Lebesgue integration, and functional analysis on an introductory level will be required in the body of the book. For theconvenience of the reader, all necessary ingredients from these areas have been included in the appendice s. Professor Deitmar is Professor of Mathematics at the University of Tbingen, Germany. He is a former Heisenberg fellow and hastaught in the U.K. for some years. Professor Echterhoff is Professor of Mathematics and Computer Science at the University of M nster, Germany |
Note: | Springer eBooks |
Contents: | Haar Integration |
Banach Algebras | |
Duality for Abelian Groups | |
The Structure of LCA | |
Groups | |
Operators on Hilbert Spaces | |
Representations | |
Compact Groups | |
Direct Integrals | |
The Selberg Trace Formula | |
The Heisenberg Group | |
SL2(?) | |
Wavelets | |
ISBN: | 9780387854694 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis |
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Call number: | SPRINGER-2009-9780387724768:ONLINE Show nearby items on shelf |
Title: | A Course in Commutative Banach Algebras [electronic resource] |
Author(s): |
Eberhard Kaniuth |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Requiring only a basic knowledge of functional analysis, topology, complex analysis, measure theory and group theory, this book provides a thorough and self-contained introduction to the theory of commutative Banach algebras. Thecore are chapters on Gelfand's theory, regularity and spectral synthesis. Special emphasis is placed on applications in abstract harmonic analysis and on treating many special classes of commutative Banach algebras, such as uniformalgebras, group algebras and Beurling algebra s, and tensor products. Detailed proofs and a variety of exercises are given. The book aims at graduate students and can be used as a text for courses on Banach algebras, with variouspossible specializations, or a Gelfand theory based course in harmonic a nalysis |
Note: | Springer eBooks |
Contents: | Preface |
General Theory of Banach Algebras | |
Gelfand Theory | |
Functional Calculus, Shilov Boundary, and Applications | |
Regularity and Related Properties | |
Spectral Synthesis and Ideal Theory | |
Appendix | |
References | |
Index | |
ISBN: | 9780387724768 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v246 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Operator theory |
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Call number: | SPRINGER-2008-9780817646837:ONLINE Show nearby items on shelf |
Title: | Representations, Wavelets, and Frames [electronic resource] : A Celebration of the Mathematical Work of Lawrence W. Baggett |
Author(s): |
Palle E. T Jorgensen Kathy D Merrill Judith A Packer |
Date: | 2008 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools they may be orthogonalor have redundancies (e. g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topicsare selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure andapplied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, andconcludes with analyses of computational schemes used in communications engineering. Within e ach section, individual chapters present new research, provide relevant background material, and point to new trends and open questions.Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornels on, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F.Taylor, E. Weber, X. Zhang |
Note: | Springer eBooks |
Contents: | Foreword |
Preface | |
Acknowledgments | |
Mathematical Family Tree of Lawrence W. Baggett | |
Publications of Lawrence W. Baggett | |
Co | |
Workers of Lawrence W. Baggett | |
Titles of All Talks | |
Classical and Abstract Harmonic Analysis | |
Frames and Multiresolution Structures | |
Wavelet Sets | |
Applications to Dynamical Systems and C* | |
Algebras | |
Signal and Image Processing | |
Symbols | |
Index | |
ISBN: | 9780817646837 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Functional analysis |
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Call number: | SPRINGER-2008-9780817646783:ONLINE Show nearby items on shelf |
Title: | Frames and Bases [electronic resource] : An Introductory Course |
Author(s): |
Ole Christensen |
Date: | 2008 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | During the last several years, frames have become increasingly popular they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of theseconstructions were based on q uite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to amore constructive one. Based on a streamlined pre sentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue betweenmathematicians and engineers. Newly added sections on applications wi ll help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in theirfield. Key features and topics: * Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers. * An introductory chapter provides basic results in finite-dimensional vector spaces,enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technica l complications in infinite-dimensional spaces. * Extensive exercises for use in theoretical graduate courses on basesand frames, or applications-oriented courses focusing on either Gabor analysis or wavelets. * Detailed description of frames with full pr oofs, an examination of the relationship between frames and Riesz bases, and a discussion ofvarious ways to construct frames. * Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connectionsto time-frequency analysis, Gabor analysis, and wavelets. Frames and Bases: An Introductory Course will be an excellent textbook |
Note: | Springer eBooks |
Contents: | Frames in Finite |
dimensional Inner Product Spaces | |
Infinite | |
dimensional Vector Spaces and Sequences | |
Bases | |
Bases and their Limitations | |
Frames in Hilbert Spaces | |
B | |
splines | |
Frames of Translates | |
Shift | |
Invariant Systems | |
Gabor Frames in L(R) | |
Gabor Frames in l(Z) | |
Wavelet Frames in L(R) | |
ISBN: | 9780817646783 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Operator theory |
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Call number: | SPRINGER-2007-9783540718970:ONLINE Show nearby items on shelf |
Title: | Stratified Lie Groups and Potential Theory for their Sub-Laplacians [electronic resource] |
Author(s): |
A Bonfiglioli E Lanconelli F Uguzzoni |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The existence, for every sub-Laplacian, of a homogeneous fundamental solution smooth out of the origin, plays a crucial role in the book. This makes it possible to develop an exhaustive Potential Theory, almost completelyparallel to that of the class ical Laplace operator. This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. In recent years, sub-Laplacian operators have received considerableattention due to their special role in the theory of linea r second-order PDE's with semidefinite characteristic form. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra ofleft-invariant vector fields. The presentation is accessible to graduate students and r equires no specialized knowledge in algebra nor in differential geometry. It is thus addressed, besides PhD students, to junior and seniorresearchers in different areas such as: partial differential equations geometric control theory geometric measure the ory and minimal surfaces in stratified Lie groups |
Note: | Springer eBooks |
Contents: | Part I: Elements of Analysis of Stratified Groups Stratified Groups and sub |
Laplacians | |
Abstract Lie Groups and Carnot Groups | |
Carnot Groups of Step Two | |
Examples of Carnot Groups | |
The Fundamental Solution for a sub | |
Laplacian and Applications | |
Part II: Elements of Potential Theory for sub | |
Laplacians Abstract Harmonic Spaces | |
The L | |
harmonic Space | |
L | |
subharmonic Functions | |
Representation Theorems | |
Maximum Principle on Unbounded Domains | |
L | |
capacity, L | |
polar Sets and Applications | |
L | |
thinness and L | |
fine Topology | |
d | |
Hausdorff Measure and L | |
capacity | |
Part III: Further Topi | |
ISBN: | 9783540718970 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Differential equations, partial , Potential theory (Mathematics) |
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Call number: | SPRINGER-2007-9780817645960:ONLINE Show nearby items on shelf |
Title: | History of Banach Spaces and Linear Operators [electronic resource] |
Author(s): |
Albrecht Pietsch |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Named for Banach, one of the great mathematicians of the twentieth century, the concept of Banach spaces figures prominently in the study of functional analysis with applications to integral and differential equations,approximation theory, harmonic a nalysis, convex geometry, numerical mathematics, analytic complexity, and probability theory. Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment ofthe history of Banach spaces and (abstract bounded) linear operators. While other historical texts on the subject focus on developments before 1950, this one is mainly devoted to the second half of the 20th century. Banach space theoryis presented in a broad mathematical context, using tools from such area s as set theory, topology, algebra, combinatorics, probability theory, and logic. Equal emphasis is given to both spaces and operators. Numerous examples andcounterexamples elucidate the scope of the underlying concepts. As a stimulus for further research , the text also contains many problems which have not been previously solved. The book may serve as a reference for researchers and as anintroduction for graduate students who want to learn Banach space theory with some historical flavor. Helpful informat ion is also provided for professors preparing their own lectures on functional analysis |
Note: | Springer eBooks |
Contents: | Preface |
Acknowledgements | |
Introduction | |
The Birth of Banach Spaces | |
Historical Roots and Basic Results | |
Weak Topologies | |
Classical Banach Spaces | |
Basic Results from the Post | |
Banach Period | |
Modern Banach Space Theory Selected Topics | |
Miscellaneous Topics | |
Mathematics is Made by Mathematicians | |
Chronology | |
Quotations | |
Bibliography | |
Index | |
ISBN: | 9780817645960 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Operator theory , Mathematics_$xHistory |
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Call number: | SPRINGER-2006-9783764376987:ONLINE Show nearby items on shelf |
Title: | The Functional Calculus for Sectorial Operators [electronic resource] |
Author(s): |
Markus Haase |
Date: | 2006 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The present monograph deals with the functional calculus for unbounded operators in general and for sectorial operators in particular. Sectorial operators abound in the theory of evolution equations, especially those of parabolictype. They satisfy a certain resolvent condition that leads to a holomorphic functional calculus based on Cauchy-type integrals. Via an abstract extension procedure, this elementary functional calculus is then extended to a large classof (even meromorphic) functions. With thi s functional calculus at hand, the book elegantly covers holomorphic semigroups, fractional powers, and logarithms. Special attention is given to perturbation results and the connection with thetheory of interpolation spaces. A chapter is devoted to the e xciting interplay between numerical range conditions, similarity problems and functional calculus on Hilbert spaces. Two chapters describe applications, for example toelliptic operators, to numerical approximations of parabolic equations, and to the maxim al regularity problem. This book is the first systematic account of a subject matter which lies in the intersection of operator theory, evolutionequations, and harmonic analysis. It is an original and comprehensive exposition of the theory as a whole. Wri tten in a clear style and optimally organised, it will prove useful for the advanced graduate as well as for the experiencedresearcher |
Note: | Springer eBooks |
Contents: | Preface |
1. Axiomatics for Functional Calculi | |
2. The Functional Calculus for Sectorial Operators | |
3. Fractional Powers and Semigroups | |
4. Strip | |
type Operators and the Logarithm | |
5. The Boundedness of the H | |
infinity | |
calculus | |
6. Interpolation Spaces | |
7. The Functional Calculus on Hilbert Spaces | |
8. Differential Operators | |
9. Mixed Topics | |
Appendices | |
Bibliography | |
Index | |
ISBN: | 9783764376987 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v169 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Operator theory |
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Call number: | SPRINGER-2006-9780817644406:ONLINE Show nearby items on shelf |
Title: | Geometric Function Theory [electronic resource] : Explorations in Complex Analysis |
Author(s): |
Steven G Krantz |
Date: | 2006 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research,including invariant ge ometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphicfunctions, the inhomogeneous CauchyRiemann equations, and the corona problem. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with anunderstanding and explanation of their interrelations with other im portant parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory.Although the book examines complex analysis from many different points of view, it uses geomet ric analysis as its unifying theme. This methodically designed book contains a rich collection of exercises, examples, and illustrationswithin each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thoroug h index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic backgroundin complex analysisand also to spark the interest of seasoned workers in the fieldthe book imparts a solid education both in complex analysi s and in how modern mathematics works |
Note: | Springer eBooks |
Contents: | Classical Function Theory |
Invariant Geometry | |
Variations on the Theme of the Schwarz Lemma | |
Normal Families | |
The Riemann Mapping Theorem and Its Generalizations | |
Boundary Regularity of Conformal Maps | |
The Boundary Behavior of Holomorphic Functions | |
Real and Harmonic Analysis | |
The Cauchy | |
Riemann Equations | |
The Greens Function and the Poisson Kernel | |
Harmonic Measure | |
Conjugate Functions and the Hilbert Transform | |
Wolffs Proof of the Corona Theorem | |
Algebraic Topics | |
Automorphism Groups of Domains in the Plane | |
Cousin Problems, Cohomology, and Sheaves | |
ISBN: | 9780817644406 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Cornerstones |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Harmonic analysis , Functions of complex variables , Differential equations, partial , Potential theory (Mathematics) , Global differential geometry |
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Call number: | SPRINGER-2005-9783540315520:ONLINE Show nearby items on shelf |
Title: | Abstract Harmonic Analysis of Continuous Wavelet Transforms [electronic resource] |
Author(s): |
Hartmut Fhr |
Date: | 2005 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated bythe discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, theconnection provides the starting point for a reasonably self-contained exposition of Plancherel theory. Therefore, the book can also be read as a problem-driven introduction to the Plancherel formula |
Note: | Springer eBooks |
Contents: | Introduction |
Wavelet Transforms and Group Representations | |
The Plancherel Transform for Locally Compact Groups | |
Plancherel Inversion and Wavelet Transforms | |
Admissible Vectors for Group Extension | |
Sampling Theorems for the Heisenberg Group | |
References | |
Index | |
ISBN: | 9783540315520 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 1617-9692 : v1863 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis |
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Call number: | SPRINGER-2004-9783662098578:ONLINE Show nearby items on shelf |
Title: | Semigroups, Boundary Value Problems and Markov Processes |
Author(s): |
Kazuaki Taira |
Date: | 2004 |
Size: | 1 online resource (340 p.) |
Note: | 10.1007/978-3-662-09857-8 |
Contents: | 1 Introduction and Main Results -- 2 Theory of Semigroups -- 3 Markov Processes and Semigroups -- 4 Theory of Distributions -- 5 Theory of Pseudo-Differential Operators -- 6 Elliptic Boundary Value Problems -- 7 Elliptic Boundary |
Value Problems and Feller Semigroups -- 8 Proof of Theorem 1.1 -- 9 Proof of Theorem 1.2 -- 10 A Priori Estimates -- 11 Proof of Theorem 1.3 -- 12 Proof of Theorem 1.4, Part (i) -- 13 Proofs of Theorem 1.5 and Theorem 1.4, Part (ii) -- | |
14 Boundary Value Problems for Waldenfels Operators -- A Boundedness of Pseudo-Differential Operators -- A.1 The Littlewood-Paley Series -- A.2 Definition of Sobolev and Besov Spaces -- A.3 Non-Regular Symbols -- A.5 Proof of | |
Proposition A.7 -- A.6 Proof of Proposition A.8 -- B Unique Solvability of Pseudo-Differential Operators -- C The Maximum Principle -- C.1 The Weak Maximum Principle -- C.2 The Strong Maximum Principle -- C.3 The Boundary Point Lemma | |
-- References -- Index of Symbols | |
ISBN: | 9783662098578 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Partial differential equations , Probabilities , Mathematics , Probability Theory and Stochastic Processes , Functional Analysis , Abstract Harmonic Analysis , Partial Differential Equations |
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Call number: | SPRINGER-2004-9783540445081:ONLINE Show nearby items on shelf |
Title: | Topics in Orbit Equivalence |
Author(s): |
Alexander S Kechris |
Date: | 2004 |
Size: | 1 online resource (138 p.) |
Note: | 10.1007/b99421 |
Contents: | Preface -- I. Orbit Equivalence -- II. Amenability and Hyperfiniteness -- III. Costs of Equivalence Relations and Groups -- References -- Index |
ISBN: | 9783540445081 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1852 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Harmonic analysis , Dynamics , Ergodic theory , Functions of real variables , Mathematical logic , Topology , Mathematics , Analysis , Mathematical Logic and Foundations , Real Functions , Dynamical Systems and Ergodic Theory , Abstract Harmonic Analysis , Topology |
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Call number: | SPRINGER-2004-9781402025259:ONLINE Show nearby items on shelf |
Title: | Fredholm and Local Spectral Theory, with Applications to Multipliers |
Author(s): |
Pietro Aiena |
Date: | 2004 |
Size: | 1 online resource (444 p.) |
Note: | 10.1007/1-4020-2525-4 |
Contents: | The Kato decomposition property -- The single-valued extension property -- The SVEP and Fredholm theory -- Multipliers of commutative Banach algebras -- Abstract Fredholm theory -- Decomposability -- Perturbation classes of operators |
ISBN: | 9781402025259 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Operator theory , Mathematics , Operator Theory , Functional Analysis , Abstract Harmonic Analysis |
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Call number: | SPRINGER-2004-9780817682125:ONLINE Show nearby items on shelf |
Title: | Sampling, Wavelets, and Tomography |
Author(s): | |
Date: | 2004 |
Size: | 1 online resource (344 p.) |
Note: | 10.1007/978-0-8176-8212-5 |
Contents: | 1 A Prelude to Sampling, Wavelets, and Tomography -- 1.1 Introduction -- 1.2 Sampling -- 1.3 Sampling and Frames -- 1.4 Wavelets and Multiresolution Analysis -- 1.5 Tomography, Spline Interpolation, and Medical Imaging -- References |
-- 2 Sampling Without Input Constraints: Consistent Reconstruction in Arbitrary Spaces -- 1 Introduction -- 2 Consistent Reconstruction -- 3 Reconstruction Scheme -- 4 Stability and Performance Analysis -- 5 Reconstruction from | |
Nonredundant Measurements -- 6 Reconstruction from Redundant Measurements -- 7 Constructing Signals with Prescribed Properties -- References -- 3 An Introduction to Irregular Weyl-Heisenberg Frames -- 1 Introduction -- 2 Preliminaries | |
-- 3 Density -- 4 Semi-Irregular Weyl—Heisenberg Frames -- 5 General Irregular Weyl—Heisenberg Frames -- 6 Concluding Remarks -- References -- 4 Robustness of Regular Sampling in Sobolev Algebras -- 1 Introduction -- 2 Wiener Amalgam | |
Spaces W(B, LP) = W(B, ?P) -- 3 Generalities on Spline-type Spaces -- 4 Sobolev Spaces ?2S -- 5 LP-Theory -- 6 Changing the Smoothness Parameter -- 7 Changing the Sampling Lattice -- 8 Jitter Stability -- References -- 5 Sampling | |
Theorems for Nonbandlimited Signals -- 1 Introduction -- 2 Signal Models -- 3 Biorthogonal Partners -- 4 Nonuniform Sampling -- 5 Derivative Sampling -- 6 Discrete-Time Case -- 7 Concluding Remarks -- References -- 6 Polynomial Matrix | |
Factorization, Multidimensional Filter Banks, and Wavelets -- 1 Introduction -- 2 Status of Results in Multivariate Polynomial Matrix Factorization -- 3 Ladder Structure of Biorthogonal Multidimensional Multiband -- 4 Sampling in | |
Wavelet Subspaces and Multiresolution Analysis -- 5 Wavelet Superresolution -- 6 Conclusions -- References -- 7 Function Spaces Based on Wavelet Expansions -- 1 Introduction -- 2 Wavelet expansions and sparseness -- 3 Robustness | |
criteria -- 4 Distributions of wavelet coefficients -- 5 Spaces Osps’ and contour-type functions -- References -- 8 Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces -- 1 Introduction and Preliminaries -- 2 | |
Construction and Characterization of the Frame Multiwavelet Vector Sets Associated with a GFMRA -- 3 Examples of GFMRAs -- References -- 9 Sampling Theory and Parallel-Beam Tomography -- 1 Introduction -- 2 The Two-Dimensional Radon | |
Transform -- 3 Sampling Lattices for the Radon Transform -- 4 The Support of (Rf) -- 5 Sampling Conditions -- 6 The Filtered Backprojection Algorithm -- 7 Analysis of the Effects of Undersampling -- 8 Further Developments -- References | |
-- 10 Filtered Backprojection Algorithms for Spiral Cone Beam CT -- 1 Introduction -- 2 PI Line and PI Window -- 3 An Approximate Algorithm for Cone Beam CT -- 4 An Exact Algorithm for Cone Beam CT -- 5 Practical Implementation and | |
Numerical Experiments -- 6 Selected Proofs -- References -- 11 Adaptive Irregular Sampling in Meshfree Flow Simulation -- 1 Introduction -- 2 Meshfree Particle Methods for Flow Simulation -- 3 Polyharmonic Splines -- 4 Adaptive | |
Irregular Sampling -- 5 Meshfree Flow Simulation -- References -- 12 Thin-Plate Spline Interpolation -- 1 Introduction -- 2 A Brief Review of One-Dimensional Interpolation Techniques -- 3 Interpolating with Trigonometric Polynomials -- | |
4 Piecewise Linear Interpolation -- 5 Cubic Spline Interpolation -- 6 The Two-Dimensional Thin-Plate Spline Transformation -- References | |
ISBN: | 9780817682125 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Image processing , Mathematical analysis , Analysis (Mathematics) , Harmonic analysis , Applied mathematics , Engineering mathematics , Mathematics , Applications of Mathematics , Analysis , Signal, Image and Speech Processing , Image Processing and Computer Vision , Abstract Harmonic Analysis , Appl.Mathematics/Computational Methods of Engineering |
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Call number: | SPRINGER-2004-9780817682040:ONLINE Show nearby items on shelf |
Title: | Noncommutative Harmonic Analysis In Honor of Jacques Carmona |
Author(s): | |
Date: | 2004 |
Size: | 1 online resource (509 p.) |
Note: | 10.1007/978-0-8176-8204-0 |
Contents: | Morris identities and the total residue for a system of type Ar -- A reduction theorem for the unitary dual of U(p, q) -- Symmetric spaces and star representations III. The Poincaré disc -- Local zeta functions for a class of |
symmetric spaces -- Quelques remarques sur les distributions invariantes dans les algèbres de Lie réductives -- Espace des coefficients de représentations admissibles d’un groupe réductif p-adique -- Dualité entre G/G? et Ie groupe | |
renversé ?G? -- Sur certains espaces d’homologie relative d’algèbres de Lie: cas des polarisations positives -- La formule de Plancherel pour les groupes de Lie presque algébrique réels -- Analytic continuation of nonholomorphic | |
discrete series for classical groups -- A branching law for subgroups fixed by an involution and a noncompact analogue of the Borel-Weil theorem -- Representations of SL2and the distribution of points in ?n -- A localization argument | |
for characters of reductive Lie groups: an introduction and examples -- Intertwining ladder representations for SU(p, q)into Dolbeault cohomology -- Summation formulas, from Poisson and Voronoi to the present -- McKay’s correspondence | |
and characters of finite subgroups of SU(2) -- Méthodes de Kashiwara-Vergne- Rouvière pour les espaces symétriques -- Einstein integrals and induction of relations | |
ISBN: | 9780817682040 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics : 220 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Number theory , Mathematics , Abstract Harmonic Analysis , Topological Groups, Lie Groups , Number Theory |
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Call number: | SPRINGER-2004-9780817681982:ONLINE Show nearby items on shelf |
Title: | Methods of Applied Mathematics with a MATLAB Overview |
Author(s): |
Jon H Davis |
Date: | 2004 |
Size: | 1 online resource (721 p.) |
Note: | 10.1007/978-0-8176-8198-2 |
Contents: | 1 Introduction -- 1.1 An Overview -- 1.2 Topics by Chapter -- 1.3 Applying Mathematics -- References -- 2 Fourier Series -- 2.1 Introduction -- 2.2 Inner Products and Fourier Expansions -- 2.3 Convergence of Fourier Series -- 2.4 |
Pointwise and Uniform Convergence of Fourier Series -- 2.5 Gibb’s Phenomenon and Summation Methods -- 2.6 Summation Methods -- 2.7 Fourier Series Properties -- 2.8 Periodic Solutions of Differential Equations -- 2.9 Impedance Methods | |
and Periodic Solutions -- 2.10 Power Spectrum and Parseval’s Theorem -- References -- 3 Elementary Boundary Value Problems -- 3.1 Introduction -- 3.2 The One-Dimensional Diffusion Equation -- 3.3 The Wave Equation -- 3.4 The Potential | |
Equation -- 3.5 Discrete Models of Boundary Value Problems -- 3.6 Separation of Variables -- 3.7 Half-Range Expansions and Symmetries -- 3.8 Some Matters of Detail -- References -- 4 Sturm-Liouville Theory and Boundary Value Problems | |
-- 4.1 Further Boundary Value Problems -- 4.2 Selfadjoint Eigenvalue Problems -- 4.3 Sturm-Liouville Problems -- 4.4 Power Series and Singular Sturm-Liouville Problems -- 4.5 Cylindrical Problems and Bessel’s Equation -- 4.6 | |
Multidimensional Problems and Forced Systems -- 4.7 Finite Differences and Numerical Methods -- 4.8 Variational Models and Finite Element Methods -- 4.9 Computational Finite Element Methods -- References -- 5 Functions of a Complex | |
Variable -- 5.1 Complex Variables and Analytic Functions -- 5.2 Domains of Definition of Complex Functions -- 5.3 Integrals and Cauchy’s Theorem -- 5.4 Cauchy’s Integral Formula, Taylor Series, and Residues -- 5.5 Complex Variables and | |
Fluid Flows -- 5.6 Conformal Mappings and the Principle of the Argument -- References -- 6 Laplace Transforms -- 6.1 Introduction -- 6.2 Definitions of the Laplace Transform -- 6.3 Mechanical Properties of Laplace Transforms -- 6.4 | |
Elementary Transforms and Fourier Series Calculations -- 6.5 Elementary Applications to Differential Equations -- 6.6 Convolutions, Impulse Responses, and Weighting Patterns -- 6.7 Vector Differential Equations -- 6.8 Impedance Methods | |
-- References -- 7. Fourier Transforms -- 7.1 Introduction -- 7.2 Basic Fourier Transforms -- 7.3 Formal Properties of Fourier Transforms -- 7.4 Convolutions and Parseval’s Theorem -- 7.5 Comments on the Inversion Theorem -- 7.6 | |
Fourier Inversion by Contour Integration -- 7.7 The Laplace Transform Inversion Integral -- 7.8 An Introduction to Generalized Functions -- 7.9 Fourier Transforms, Differential Equations and Circuits -- 7.10 Transform Solutions of | |
Boundary Value Problems -- 7.11 Band-limited Functions and Communications -- References -- 8 Discrete Variable Transforms -- 8.1 Some Discrete Variable Models -- 8.2 Z-Transforms -- 8.3 Z-Transform Properties -- 8.4 z-Transform | |
Inversion Integral -- 8.5 Discrete Fourier Transforms -- 8.6 Discrete Fourier Transform Properties -- 8.7 Some Applications of Discrete Transform Methods -- 8.8 Finite and Fast Fourier Transforms -- 8.9 Finite Fourier Properties -- | |
8.10 Fast Finite Transform Algorithm -- 8.11 Computing The 1-1.1 -- References -- 9 Additional Topics -- 9.1 Local Waveform Analysis -- 9.2 Uncertainty Principle -- 9.3 Short-Time Fourier Transforms -- 9.4 Function Shifts and Scalings | |
-- 9.5 Orthonormal Shifts -- 9.6 Multi-Resolution Analysis and Wavelets -- 9.7 On Wavelet Applications -- 9.8 Two-Sided Transforms -- 9.9 Walsh Functions -- 9.10 Geometrically Based Transforms -- References -- A Linear Algebra Overview | |
-- A.1 Vector spaces -- A.2 Linear Mappings -- A.3 Inner Products -- A.4 Linear Functionals and Dual Spaces -- A.5 Canonical Forms -- References -- B Software Resources -- B.1 Computational and Visualization Software -- B.2 MATLAB Data | |
Structures -- B.3 MATLAB Operators and Syntax -- B.4 MATLAB Programming Structures -- B.5 MATLAB Programs and Scripts -- B.6 Common Idioms -- B.7 Graphics -- B.8 Toolboxes and Enhancemants -- References -- C Transform Tables -- C.1 | |
Laplace Transforms -- C.2 Fourier Transforms -- C.3 Z Transforms -- C.4 Discrete Fourier Transforms | |
ISBN: | 9780817681982 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Functions of complex variables , Applied mathematics , Engineering mathematics , Computer mathematics , Physics , Mathematics , Fourier Analysis , Computational Mathematics and Numerical Analysis , Theoretical, Mathematical and Computational Physics , Applications of Mathematics , Abstract Harmonic Analysis , Functions of a Complex Variable |
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Call number: | SPRINGER-2004-9780817681920:ONLINE Show nearby items on shelf |
Title: | Lie Theory Lie Algebras and Representations |
Author(s): |
Jens Carsten Jantzen |
Date: | 2004 |
Size: | 1 online resource (331 p.) |
Note: | 10.1007/978-0-8176-8192-0 |
Contents: | Preface -- Nilpotent Orbits in Representation Theory -- 1 Nilpotent Orbits for Classical Groups -- 2 Some General Results -- 3 Centralizers in the Classical Cases -- 4 Bala-Carter Theory -- 5 Centralizers -- 6 The Nilpotent Cone I -- |
7 The Nilpotent Cone II -- 8 Functions on Orbits and Orbit Closures -- 9 Associated Varieties -- 10 Springer’s Fibers and Steinberg’s Triples -- 11 Paving Springer’s Fibers -- 12 ?-adic and Perverse Stuff -- 13 Springer’s | |
Representations -- References -- Infinite-Dimensional Groups and Their Representations -- I The Finite-Dimensional Case -- II Split Lie Algebras -- III Unitary Highest Weight Modules -- IV Banach-Lie Groups -- V Holomorphic | |
Representations of Classical Banach-Lie Groups -- VI Geometry of Coadjoint Orbits of Banach-Lie Groups -- VII Coadjoint Orbits and Complex Line Bundles for U2(H) -- Appendix: The Topology of Classical Banach-Lie Groups -- References | |
ISBN: | 9780817681920 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics : 228 |
Keywords: | Mathematics , Algebra , Group theory , Topological groups , Lie groups , Harmonic analysis , Geometry , Number theory , Mathematics , Topological Groups, Lie Groups , Algebra , Group Theory and Generalizations , Abstract Harmonic Analysis , Geometry , Number Theory |
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Call number: | SPRINGER-2004-9780817681883:ONLINE Show nearby items on shelf |
Title: | Köthe-Bochner Function Spaces |
Author(s): |
Pei-Kee Lin |
Date: | 2004 |
Size: | 1 online resource (370 p.) |
Note: | 10.1007/978-0-8176-8188-3 |
Contents: | 1 Classical Theorems -- 1.1 Preliminaries -- 1.2 Basic Sequences -- 1.3 Banach Spaces Containing l1 or c0 -- 1.4 James’s Theorem -- 1.5 Continuous Function Spaces -- 1.6 The Dunford-Pettis Property -- 1.7 The Pe?czynski Property (V*) |
-- 1.8 Tensor Products of Banach Spaces -- 1.9 Conditional Expectation and Martingales -- 1.10 Notes and Remarks -- 1.11 References -- 2 Convexity and Smoothness -- 2.1 Strict Convexity and Uniform Convexity -- 2.2 Smoothness -- 2.3 | |
Banach-Saks Property -- 2.4 Notes and Remarks -- 2.5 References -- 3 Köthe-Bochner Function Spaces -- 3.1 Köthe Function Spaces -- 3.2 Strongly and Scalarly Measurable Functions -- 3.3 Vector Measure -- 3.4 Some Basic Results -- 3.5 | |
Dunford-Pettis Operators -- 3.6 The Radon-Nikodým Property -- 3.7 Notes and Remarks -- 3.8 References -- 4 Stability Properties I -- 4.1 Extreme Points and Smooth Points -- 4.2 Strongly Extreme and Denting Points -- 4.3 Strongly and | |
w*-Strongly Exposed Points -- 4.4 Notes and Remarks -- 4.5 References -- 5 Stability Properties II -- 5.1 Copies of c0 in E(X) -- 5.2 The Díaz-Kalton Theorem -- 5.3 Talagrand’s L1(X)-Theorem -- 5.4 Property (V*) -- 5.5 The Talagrand | |
Spaces -- 5.6 The Banach-Saks Property -- 5.7 Notes and Remarks -- 5.8 References -- 6 Continuous Function Spaces -- 6.1 Vector-Valued Continuous Functions -- 6.2 The Dieudonné Property in C(K, X) -- 6.3 The Hereditary Dunford-Pettis | |
Property -- 6.4 Projective Tensor Products -- 6.5 Notes and Remarks -- 6.6 References | |
ISBN: | 9780817681883 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Harmonic analysis , Functional analysis , Operator theory , Functions of real variables , Probabilities , Mathematics , Functional Analysis , Analysis , Abstract Harmonic Analysis , Operator Theory , Real Functions , Probability Theory and Stochastic Processes |
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Call number: | SPRINGER-2004-9780817681722:ONLINE Show nearby items on shelf |
Title: | Fourier Analysis and Convexity |
Author(s): | |
Date: | 2004 |
Size: | 1 online resource (268 p.) |
Note: | 10.1007/978-0-8176-8172-2 |
Contents: | Lattice Point Problems: Crossroads of Number Theory, Probability Theory and Fourier Analysis -- Totally Geodesic Radon Transform of LP-Functions on Real Hyperbolic Space -- Fourier Techniques in the Theory of Irregularities of Point |
Distribution -- Spectral Structure of Sets of Integers -- 100 Years of Fourier Series and Spherical Harmonics in Convexity -- Fourier Analytic Methods in the Study of Projections and Sections of Convex Bodies -- The Study of | |
Translational Tiling with Fourier Analysis -- Discrete Maximal Functions and Ergodic Theorems Related to Polynomials -- What Is It Possible to Say About an Asymptotic of the Fourier Transform of the Characteristic Function of a | |
Two-dimensional Convex Body with Nonsmooth Boundary? -- SomeRecent Progress on the Restriction Conjecture -- Average Decayof the Fourier Transform | |
ISBN: | 9780817681722 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Functional analysis , Convex geometry , Discrete geometry , Number theory , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Convex and Discrete Geometry , Number Theory , Functional Analysis |
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Call number: | SPRINGER-2004-9780817681647:ONLINE Show nearby items on shelf |
Title: | An Introduction to the Uncertainty Principle Hardy’s Theorem on Lie Groups |
Author(s): |
Sundaram Thangavelu |
Date: | 2004 |
Size: | 1 online resource (174 p.) |
Note: | 10.1007/978-0-8176-8164-7 |
Contents: | 1 Euclidean Spaces -- 1.1 Fourier transform on L1(?n) -- 1.2 Hermite functions and L2 theory -- 1.3 Spherical harmonics and symmetry properties -- 1.4 Hardy’s theorem on ?n -- 1.5 Beurling’s theorem and its consequences -- 1.6 Further |
results and open problems -- 2 Heisenberg Groups -- 2.1 Heisenberg group and its representations -- 2.2 Fourier transform on Hn -- 2.3 Special Hermite functions -- 2.4 Fourier transform of radial functions -- 2.5 Unitary group and | |
spherical harmonics -- 2.6 Spherical harmonics and the Weyl transform -- 2.7 Weyl correspondence of polynomials -- 2.8 Heat kernel for the sublaplacian -- 2.9 Hardy’s theorem for the Heisenberg group -- 2.10 Further results and open | |
problems -- 3 Symmetric Spaces of Rank 1 -- 3.1 A Riemannian space associated to Hn -- 3.2 The algebra of radial functions on S -- 3.3 Spherical Fourier transform -- 3.4 Helgason Fourier transform -- 3.5 Hecke-Bochner formula for the | |
Helgason Fourier transform -- 3.6 Jacobi transforms -- 3.7 Estimating the heat kernel -- 3.8 Hardy’s theorem for the Helgason Fourier transform -- 3.9 Further results and open problems | |
ISBN: | 9780817681647 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics : 217 |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Functional analysis , Functions of complex variables , Mathematics , Abstract Harmonic Analysis , Fourier Analysis , Functional Analysis , Several Complex Variables and Analytic Spaces |
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Call number: | SPRINGER-2003-9783034880350:ONLINE Show nearby items on shelf |
Title: | Function Spaces, Differential Operators and Nonlinear Analysis The Hans Triebel Anniversary Volume |
Author(s): | |
Date: | 2003 |
Size: | 1 online resource (476 p.) |
Note: | 10.1007/978-3-0348-8035-0 |
Contents: | Spaces of differentiable functions -- Entropy, embeddings and equations -- Nonvariational elliptic systems via Galerkin methods -- Superposition operators in Zygmund and BMO spaces -- Asymptotics of a singular solution to the |
Dirichlet problem for an elliptic equation with discontinuous coefficients near the boundary -- Weighted Hardy spaces on a domain and its application -- The general blow-up for nonlinear PDE’s -- Laplace and Schrodinger operators on | |
regular metric trees: the discrete spectrum case -- Inverse boundary problems in two dimensions -- On the regularity of weak solutions of elliptic systems in Banach spaces -- Complements and results on h-sets -- Lifting properties of | |
Sobolev spaces -- Sharp estimates of approximation numbers via growth envelopes -- Sharp summability of functions from Orlicz-Sobolev spaces -- Regularity problems for some semi-linear problems -- Besov Regularity for the Neumann | |
Problem -- Intrinsic descriptions using means of differences for Besov spaces on Lipschitz domains -- Landesman-Lazer type like results for the p-Laplacian -- On the Sobolev, Hardy and CLR inequalities associated with Schrödinger | |
operators -- Mazur distance and normal structure in Banach spaces -- Some inequalities for integral operators, associated with the Bessel differential operator -- On determining individual behaviour from population data -- Nonlocal | |
investigations of inhomogeneous indefinite elliptic equations via variational methods -- Regularity results and parametrices of semi-linear boundary problems of product type -- Potential estimates for large solutions of semilinear | |
elliptic equations -- Coarea properties of Sobolev functions -- Banach envelopes of the Besov and Triebel-Lizorkin spaces and applications to PDE’s -- On the flow map for a class of parabolic equations -- Spaces of functions with | |
bounded and vanishing mean oscillation -- On equivalent quasi-norms on Lorentz spaces -- Concave functions of second order elliptic operators, kernel estimates and applications -- On approximation of solutions of parabolic functional | |
differential equations in unbounded domains -- Function spaces in presence of symmetries: compactness of embeddings, regularity and decay of functions -- Participants FSDONA-Ol | |
ISBN: | 9783034880350 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Harmonic analysis , Fourier analysis , Functional analysis , Operator theory , Partial differential equations , Mathematics , Analysis , Fourier Analysis , Functional Analysis , Operator Theory , Partial Differential Equations , Abstract Harmonic Analysis |
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Call number: | SPRINGER-2002-9789401599221:ONLINE Show nearby items on shelf |
Title: | Bounded and Compact Integral Operators |
Author(s): |
David E Edmunds |
Date: | 2002 |
Size: | 1 online resource (643 p.) |
Note: | 10.1007/978-94-015-9922-1 |
Contents: | 1. Hardy-Type Operators -- 2. Fractional Integrals on the Line -- 3. One-Sided Maximal Functions -- 4. Ball Fractional Integrals -- 5. Potentials on RN -- 6. Fractional Integrals on Measure Spaces -- 7. Singular Numbers -- 8. Singular |
Integrals -- 9. Multipliers of Fourier Transforms -- 10. Problems -- References | |
ISBN: | 9789401599221 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 543 |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Integral transforms , Operational calculus , Operator theory , Potential theory (Mathematics) , Mathematics , Potential Theory , Fourier Analysis , Abstract Harmonic Analysis , Integral Transforms, Operational Calculus , Operator Theory |
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Call number: | SPRINGER-2002-9783540477938:ONLINE Show nearby items on shelf |
Title: | Harmonic Functions on Groups and Fourier Algebras |
Author(s): |
Cho-Ho Chu |
Date: | 2002 |
Size: | 1 online resource (100 p.) |
Note: | 10.1007/b83280 |
Contents: | 1. Introduction -- 2. Harmonic functions on locally compact groups: 2.1. Preliminaries and notation. 2.2. Poisson representation of harmonic functions. 2.3. Semigroup structures of the Poisson space. 2.4. Almost periodic harmonic |
functions. 2.5. Distal harmonic functions. 2.6. Transitive group actions on Poisson spaces. 2.7. Examples -- 3. Harmonic functionals on Fourier algebras: 3.1. Fourier algebras. 3.2. Harmonic functionals and associated ideals. 3.3. | |
Jordan structures of harmonic functionals. 3.4. Classification of harmonic functionals -- References -- List of symbols -- Index | |
ISBN: | 9783540477938 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1782 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Functional analysis , Integral equations , Potential theory (Mathematics) , Functions of complex variables , Mathematics , Abstract Harmonic Analysis , Potential Theory , Integral Equations , Topological Groups, Lie Groups , Functional Analysis , Several Complex Variables and Analytic Spaces |
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Call number: | SPRINGER-2002-9783540455608:ONLINE Show nearby items on shelf |
Title: | Lectures on Amenability |
Author(s): |
Volker Runde |
Date: | 2002 |
Size: | 1 online resource (302 p.) |
Note: | 10.1007/b82937 |
Contents: | Paradoxical decompositions -- Amenable, locally comact groups -- Amenable Banach algebras -- Exemples of amenable Banach algebras -- Amenability-like properties -- Banach homology -- C* and W*-algebras -- Operator amenability -- |
Geometry of spaces of homomorphisms -- Open problems: Abstract harmonic analysis -- Tensor products -- Banach space properties -- Operator spaces -- List of symbols -- References -- Index | |
ISBN: | 9783540455608 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1774 |
Keywords: | Mathematics , Algebra , Category theory (Mathematics) , Homological algebra , Harmonic analysis , Functional analysis , Global analysis (Mathematics) , Manifolds (Mathematics) , Mathematics , Algebra , Functional Analysis , Abstract Harmonic Analysis , Category Theory, Homological Algebra , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2002-9783034882156:ONLINE Show nearby items on shelf |
Title: | Interpolation Theory, Systems Theory and Related Topics The Harry Dym Anniversary Volume |
Author(s): | |
Date: | 2002 |
Size: | 1 online resource (414 p.) |
Note: | 10.1007/978-3-0348-8215-6 |
Contents: | Looking Back -- List of Publications of Harry Dym -- On Joint Work with Harry Dym -- Methods of Krein Space Operator Theory -- Notes on Interpolation in the Generalized Schur Class.I. Applications of Realization Theory -- Stable |
Dissipative Linear Stationary Dynamical Scattering Systems -- Concrete Interpolation of Meromorphic Matrix Functions on Riemann Surfaces -- On Realizations of Rational Matrix Functions of Several Complex Variables -- The Poincaré—Hardy | |
Inequality on the Complement of a Cantor Set -- Finite Section Method for Linear Ordinary Differential Equations on the Full Line -- On the Spectral Radius of Multi-Matrix Functions -- A Generic Schur Function is an Inner One -- | |
Abstract Interpolation Scheme for Harmonic Functions -- Chains of Space-Time Open Systems and DNA -- A Class of Robustness Problems in Matrix Analysis -- Dual Discrete Canonical Systems and Dual Orthogonal Polynomials -- | |
Non-Selfadjoint Sturm-Liouville Operators with Multiple Spectra | |
ISBN: | 9783034882156 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications : 134 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis |
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Call number: | SPRINGER-2002-9781475752885:ONLINE Show nearby items on shelf |
Title: | Functional Equations — Results and Advances |
Author(s): | |
Date: | 2002 |
Size: | 1 online resource (361 p.) |
Note: | 10.1007/978-1-4757-5288-5 |
Contents: | I. Classical Functional Equations and Inequalities -- On some trigonometric functional inequalities -- On the continuity of additive—like functions and Jensen convex functions which are Borel on a sphere -- Note on a |
functional—differential inequality -- A characterization of stationary sets for the class of Jensen convex functions -- On the characterization of Weierstrass’s sigma function -- On a Mikusi?ski—Jensen functional equation -- II. | |
Stability of Functional Equations -- Stability of the multiplicative Cauchy equation in ordered fields -- On approximately monomial functions -- Les opérateurs de Hyers -- Geometrical aspects of stability -- III. Functional Equations | |
in One Variable and Iteration Theory -- On semi-conjugacy equation for homeomorphisms of the circle -- A survey of results and open problems on the Schilling equation -- Properties of an operator acting on the space of bounded real | |
functions and certain subspaces -- IV. Composite Functional Equations and Theory of Means -- A Matkowski-Sutô type problem for quasi-arithmetic means of order ? -- An extension theorem for conjugate arithmetic means -- Homogeneous | |
Cauchy mean values -- On invariant generalized Beckenbach-Gini means -- Final part of the answer to a Hilbert’s question -- V. Functional Equations on Algebraic Structures -- A generalization of d’Alembert’s functional equation -- | |
About a remarkable functional equation on some restricted domains -- On discrete spectral synthesis -- Hyers theorem and the cocycle property -- VI. Functional Equations in Functional Analysis -- Mappings whose derivatives are | |
isometries -- Localizable functionals -- Jordan maps on standard operator algebras -- VII. Bisymmetry and Associativity Type Equations on Quasigroups -- On the functional equation S1(x, y) = S2(x, T(N(x), y)) -- Generalized | |
associativity on rectangular quasigroups -- The aggregation equation: solutions with non intersecting partial functions | |
ISBN: | 9781475752885 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Advances in Mathematics : 3 |
Keywords: | Mathematics , Harmonic analysis , Difference equations , Functional equations , Functional analysis , Sequences (Mathematics) , Special functions , Mathematics , Difference and Functional Equations , Sequences, Series, Summability , Functional Analysis , Abstract Harmonic Analysis , Special Functions |
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Call number: | SPRINGER-2001-9789401730617:ONLINE Show nearby items on shelf |
Title: | Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups Structural Properties and Limit Theorems |
Author(s): |
Wilfried Hazod |
Date: | 2001 |
Size: | 1 online resource (612 p.) |
Note: | 10.1007/978-94-017-3061-7 |
Contents: | I Probabilities on vector spaces -- II Probabilities on simply connected nilpotent Lie groups -- III (Semi-) stability and limit theorems on general locally compact groups -- Epilogue -- List of Symbols |
ISBN: | 9789401730617 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 531 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Functional analysis , Measure theory , Probabilities , Mathematics , Probability Theory and Stochastic Processes , Topological Groups, Lie Groups , Abstract Harmonic Analysis , Measure and Integration , Functional Analysis |
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Call number: | SPRINGER-2001-9789401597975:ONLINE Show nearby items on shelf |
Title: | Asymptotics of Linear Differential Equations |
Author(s): |
M. H Lantsman |
Date: | 2001 |
Size: | 1 online resource (441 p.) |
Note: | 10.1007/978-94-015-9797-5 |
Contents: | 1. Introduction -- 2. Metric spaces -- 3. Asymptotic spaces -- 4. Asymptotic behaviour of functions -- 5. Power order growth functions on the positive semi-axis -- 6. Power order growth functions of the complex argument -- 7. |
Integrals -- 8. Linear differential equations -- 9. General asymptotic properties of linear differential equations -- 10. Linear differential equations with power order growth coefficients on the positive semi-axis -- 11. Linear | |
differential equations in singular cases on the positive semi-axis -- 12. Linear differential equations in a sector of the complex plane -- 13. Linear differential equations with power-logarithmic coefficients -- 14. Linear difference | |
equations. General theory -- 15. Asymptotic behaviour of solutions of linear difference equations -- 16. Supplement -- List of symbols | |
ISBN: | 9789401597975 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 533 |
Keywords: | Mathematics , Harmonic analysis , Difference equations , Functional equations , Operator theory , Differential equations , Sequences (Mathematics) , Mathematics , Ordinary Differential Equations , Difference and Functional Equations , Operator Theory , Abstract Harmonic Analysis , Sequences, Series, Summability |
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Call number: | SPRINGER-2001-9783540445630:ONLINE Show nearby items on shelf |
Title: | Similarity Problems and Completely Bounded Maps Second, Expanded Edition |
Author(s): |
Gilles Pisier |
Date: | 2001 |
Size: | 1 online resource (202 p.) |
Note: | 10.1007/b55674 |
Contents: | Introduction. Description of contents -- Von Neumann's inequality and Ando's generalization -- Non-unitarizable uniformly bounded group representations -- Completely bounded maps -- Completely bounded homomorphisms and derivations -- |
Schur multipliers and Grothendieck's inequality -- Hankelian Schur multipliers. Herz-Schur multipliers -- The similarity problem for cyclic homomorphisms on a C*-algebra -- Completely bounded maps in the Banach space setting -- The Sz | |
-- Nagy-Halmos similarity problem -- The Kadison Similarity Problem -- References -- Subject Index -- Notation Index | |
ISBN: | 9783540445630 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1618 |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Mathematics , Functional Analysis , Abstract Harmonic Analysis |
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Call number: | SPRINGER-2001-9783034805698:ONLINE Show nearby items on shelf |
Title: | The Structure of Functions |
Author(s): |
Hans Triebel |
Date: | 2001 |
Size: | 1 online resource (425 p.) |
Note: | 10.1007/978-3-0348-0569-8 |
Contents: | Preface -- I Decompositions of Functions -- II Sharp Inequalities -- III Fractal Elliptic Operators -- IV Truncations and Semi-linear Equations -- References -- Symbols -- Index |
ISBN: | 9783034805698 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Measure theory , Operator theory , Partial differential equations , Mathematics , Functional Analysis , Measure and Integration , Abstract Harmonic Analysis , Partial Differential Equations , Operator Theory |
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Call number: | SPRINGER-2000-9789401141086:ONLINE Show nearby items on shelf |
Title: | Introduction to Infinite Dimensional Stochastic Analysis |
Author(s): |
Zhi-yuan Huang |
Date: | 2000 |
Size: | 1 online resource (296 p.) |
Note: | 10.1007/978-94-011-4108-6 |
Contents: | I Foundations of Infinite Dimensional Analysis -- §1. Linear operators on Hilbert spaces -- §2. Fock spaces and second quantization -- §3. Countably normed spaces and nuclear spaces -- §4. Borel measures on topological linear spaces |
-- II Malliavin Calculus -- §1. Gaussian probability spaces and Wiener chaos decomposition -- §2. Differential calculus of functionals, gradient and divergence operators -- §3. Meyer’s inequalities and some consequences -- §4. | |
Densities of non-degenerate functionals -- III Stochastic Calculus of Variation for Wiener Functionals -- §1. Differential calculus of Itô functionals and regularity of heat kernels -- §2. Potential theory over Wiener spaces and | |
quasi-sure analysis -- §3. Anticipating stochastic calculus -- IV General Theory of White Noise Analysis -- §1. General framework for white noise analysis -- §2. Characterization of functional spaces -- §3. Products and Wick products | |
of functionals -- §4. Moment characterization of distributions and positive distributions -- V Linear Operators on Distribution Spaces -- §1. Analytic calculus for distributions -- §2. Continuous linear operators on distribution spaces | |
-- §3. Integral kernel operators and integral kernel representation for operators -- §4. Applications to quantum physics -- Appendix A Hermite polynomials and Hermite functions -- Appendix B Locally convex spaces amd their dual spaces | |
-- 1. Semi-norms, norms and H-norms -- 2. Locally convex topological linear spaces, bounded sets -- 3. Projective topologies and projective limits -- 4. Inductive topologies and inductive limits -- 5. Dual spaces and weak topologies -- | |
6. Compatibility and Mackey topology -- 7. Strong topologies and reflexivity -- 8. Dual maps -- 9. Uniformly convex spaces and Banach-Saks’ theorem -- Comments -- References -- Index of Symbols | |
ISBN: | 9789401141086 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 502 |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Operator theory , Applied mathematics , Engineering mathematics , Probabilities , Mathematics , Probability Theory and Stochastic Processes , Functional Analysis , Operator Theory , Applications of Mathematics , Abstract Harmonic Analysis |
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