A Course In Abstract Harmonic Analysis
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A Course In Abstract Harmonic Analysis
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Author : Gerald B. Folland
language : en
Publisher: CRC Press
Release Date : 1994-12-27
A Course In Abstract Harmonic Analysis written by Gerald B. Folland and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-27 with Mathematics categories.
Abstract theory remains an indispensable foundation for the study of concrete cases. It shows what the general picture should look like and provides results that are useful again and again. Despite this, however, there are few, if any introductory texts that present a unified picture of the general abstract theory. A Course in Abstract Harmonic Analysis offers a concise, readable introduction to Fourier analysis on groups and unitary representation theory. After a brief review of the relevant parts of Banach algebra theory and spectral theory, the book proceeds to the basic facts about locally compact groups, Haar measure, and unitary representations, including the Gelfand-Raikov existence theorem. The author devotes two chapters to analysis on Abelian groups and compact groups, then explores induced representations, featuring the imprimitivity theorem and its applications. The book concludes with an informal discussion of some further aspects of the representation theory of non-compact, non-Abelian groups.
A Course In Abstract Harmonic Analysis
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Author : Gerald B. Folland
language : en
Publisher: CRC Press
Release Date : 2016-02-03
A Course In Abstract Harmonic Analysis written by Gerald B. Folland and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-03 with Mathematics categories.
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
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.
A First Course In Harmonic Analysis
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Author : Anton Deitmar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A First Course In 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 2013-04-17 with Mathematics categories.
This book is intended as a primer in harmonic analysis at the un dergraduate level. All the central concepts of harmonic analysis are introduced without too much technical overload. For example, the book is based entirely on the Riemann integral instead of the more demanding Lebesgue integral. Furthermore, all topological questions are dealt with purely in the context of metric spaces. It is quite sur prising that this works. Indeed, it turns out that the central concepts theory can be explained using very little of this beautiful and useful technical background. The first aim of this book is to give a lean introduction to Fourier analysis, leading up to the Poisson summation formula. The sec ond aim is to make the reader aware of the fact that both principal incarnations of Fourier Theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The third goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
Harmonic Analysis And Applications
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Author : John J. Benedetto
language : en
Publisher: CRC Press
Release Date : 1996-07-29
Harmonic Analysis And Applications written by John J. Benedetto and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-29 with Mathematics categories.
Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject. This book is about classical harmonic analysis - a textbook suitable for students, and an essay and general reference suitable for mathematicians, physicists, and others who use harmonic analysis. Throughout the book, material is provided for an upper level undergraduate course in harmonic analysis and some of its applications. In addition, the advanced material in Harmonic Analysis and Applications is well-suited for graduate courses. The course is outlined in Prologue I. This course material is excellent, not only for students, but also for scientists, mathematicians, and engineers as a general reference. Chapter 1 covers the Fourier analysis of integrable and square integrable (finite energy) functions on R. Chapter 2 of the text covers distribution theory, emphasizing the theory's useful vantage point for dealing with problems and general concepts from engineering, physics, and mathematics. Chapter 3 deals with Fourier series, including the Fourier analysis of finite and infinite sequences, as well as functions defined on finite intervals. The mathematical presentation, insightful perspectives, and numerous well-chosen examples and exercises in Harmonic Analysis and Applications make this book well worth having in your collection.
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory
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Author : Roger Howe
language : en
Publisher: World Scientific
Release Date : 2007
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory written by Roger Howe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume carries the same title as that of an international conference held at the National University of Singapore, 9OCo11 January 2006 on the occasion of Roger E. Howe''s 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe''s mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications. Sample Chapter(s). Foreword (21 KB). Chapter 1: The Theta Correspondence Over R (342 KB). Contents: The Theta Correspondence over R (J Adams); The Heisenberg Group, SL (3, R), and Rigidity (A iap et al.); Pfaffians and Strategies for Integer Choice Games (R Evans & N Wallach); When is an L -Function Non-Vanishing in Part of the Critical Strip? (S Gelbart); Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L -Functions (M Harris); The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group (T Kobayashi & G Mano); Classification des S(r)ries Discr tes pour Certains Groupes Classiques p- Adiques (C Moeglin); Some Algebras of Essentially Compact Distributions of a Reductive p -Adic Group (A Moy & M Tadic); Annihilators of Generalized Verma Modules of the Scalar Type for Classical Lie Algebras (T Oshima); Branching to a Maximal Compact Subgroup (D A Vogan, Jr.); Small Semisimple Subalgebras of Semisimple Lie Algebras (J F Willenbring & G J Zuckerman). Readership: Graduate students and research mathematicians in harmonic analysis, group representations, automorphic forms and invariant theory."
An Introduction To Harmonic Analysis
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Author : Yitzhak Katznelson
language : en
Publisher:
Release Date : 1968
An Introduction To Harmonic Analysis written by Yitzhak Katznelson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Harmonic analysis categories.
Frames And Bases
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Author : Ole Christensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-05
Frames And Bases written by Ole Christensen 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 2008-06-05 with Mathematics categories.
Based on a streamlined presentation of the author’s successful work, An Introduction to Frames and Riesz Bases, this book develops frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. The book presents basic results in an accessible way and includes extensive exercises.
A Basis Theory Primer
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Author : Christopher Heil
language : en
Publisher: Springer Science & Business Media
Release Date : 2011
A Basis Theory Primer written by Christopher Heil 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 with Mathematics categories.
This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in 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. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.
Classical And Multilinear Harmonic Analysis
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Author : Camil Muscalu
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-31
Classical And Multilinear Harmonic Analysis written by Camil Muscalu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-31 with Mathematics categories.
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.