Principles Of Harmonic Analysis
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Principles Of Harmonic Analysis
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Author : Anton Deitmar
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-21
Principles Of Harmonic Analysis written by Anton Deitmar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-21 with Mathematics categories.
The tread of this book is formed by two fundamental principles of Harmonic Analysis: the Plancherel Formula and the Poisson S- mation Formula. We ?rst prove both for locally compact abelian groups. For non-abelian groups we discuss the Plancherel Theorem in the general situation for Type I groups. The generalization of the Poisson Summation Formula to non-abelian groups is the S- berg Trace Formula, which we prove for arbitrary groups admitting uniform lattices. As examples for the application of the Trace F- mula we treat the Heisenberg group and the group SL (R). In the 2 2 former case the trace formula yields a decomposition of the L -space of the Heisenberg group modulo a lattice. In the case SL (R), the 2 trace formula is used to derive results like the Weil asymptotic law for hyperbolic surfaces and to provide the analytic continuation of the Selberg zeta function. We ?nally include a chapter on the app- cations of abstract Harmonic Analysis on the theory of wavelets. The present book is a text book for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up of the First Course in Harmonic Analysis, [9], or indep- dently, if the students have required a modest knowledge of Fourier Analysis already. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in [9].
Principles Of Harmonic Analysis
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Author : Walter Piston
language : en
Publisher:
Release Date : 1933
Principles Of Harmonic Analysis written by Walter Piston and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1933 with categories.
Principles Of Harmonic Analysis
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Author : Anton Deitmar
language : en
Publisher: Springer
Release Date : 2014-06-21
Principles Of Harmonic Analysis written by Anton Deitmar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-21 with Mathematics categories.
This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.
The Uncertainty Principle In Harmonic Analysis
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Author : Victor Havin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Uncertainty Principle In Harmonic Analysis written by Victor Havin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose).
Principles Of Harmonic Analysis
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Author : Walter Piston
language : en
Publisher:
Release Date : 1933
Principles Of Harmonic Analysis written by Walter Piston and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1933 with Harmony categories.
Harmonic And Complex Analysis In Several Variables
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Author : Steven G. Krantz
language : en
Publisher: Springer
Release Date : 2017-09-20
Harmonic And Complex Analysis In Several Variables written by Steven G. Krantz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-20 with Mathematics categories.
Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.
Symplectic Methods In Harmonic Analysis And In Mathematical Physics
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Author : Maurice A. de Gosson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-30
Symplectic Methods In Harmonic Analysis And In Mathematical Physics written by Maurice A. de Gosson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-30 with Mathematics categories.
The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
Harmonic Analysis On Commutative Spaces
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Author : Joseph Albert Wolf
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Harmonic Analysis On Commutative Spaces written by Joseph Albert Wolf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.
Harmonic Analysis On Homogeneous Spaces
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Author : Nolan R. Wallach
language : en
Publisher: Courier Dover Publications
Release Date : 2018-12-12
Harmonic Analysis On Homogeneous Spaces written by Nolan R. Wallach and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Mathematics categories.
This book is suitable for advanced undergraduate and graduate students in mathematics with a strong background in linear algebra and advanced calculus. Early chapters develop representation theory of compact Lie groups with applications to topology, geometry, and analysis, including the Peter-Weyl theorem, the theorem of the highest weight, the character theory, invariant differential operators on homogeneous vector bundles, and Bott's index theorem for such operators. Later chapters study the structure of representation theory and analysis of non-compact semi-simple Lie groups, including the principal series, intertwining operators, asymptotics of matrix coefficients, and an important special case of the Plancherel theorem. Teachers will find this volume useful as either a main text or a supplement to standard one-year courses in Lie groups and Lie algebras. The treatment advances from fairly simple topics to more complex subjects, and exercises appear at the end of each chapter. Eight helpful Appendixes develop aspects of differential geometry, Lie theory, and functional analysis employed in the main text.
Methods Of Applied Fourier Analysis
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Author : Jayakumar Ramanathan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Methods Of Applied Fourier Analysis written by Jayakumar Ramanathan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.