Non Abelian Harmonic Analysis

Author : Roger E. Howe,Eng Chye Tan
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461392002

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Non-Abelian Harmonic Analysis by Roger E. Howe,Eng Chye Tan Pdf

This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.

Author : Roger Howe,Eng Chye Tan
Publisher : Unknown
Page : 276 pages
File Size : 51,6 Mb
Release : 1992-02-27
Category : Electronic
ISBN : 1461392012

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Non-Abelian Harmonic Analysis by Roger Howe,Eng Chye Tan Pdf

Author : Anton Deitmar,Siegfried Echterhoff
Publisher : Springer
Page : 330 pages
File Size : 55,7 Mb
Release : 2014-06-21
Category : Mathematics
ISBN : 9783319057927

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Principles of Harmonic Analysis by Anton Deitmar,Siegfried Echterhoff Pdf

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.

Author : J. Carmona,M. Vergne
Publisher : Springer
Page : 249 pages
File Size : 42,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540373650

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Non-Commutative Harmonic Analysis by J. Carmona,M. Vergne Pdf

Author : Raymond C. Fabec,Gestur Ólafsson
Publisher : Unknown
Page : 529 pages
File Size : 52,6 Mb
Release : 2014-07-06
Category : Fourier analysis
ISBN : 0991326601

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Non-Commutative Harmonic Analysis by Raymond C. Fabec,Gestur Ólafsson Pdf

This is a graduate text on harmonic analysis. It begins with a chapter on Fourier series. The next two chapters are spent covering function theory on real spaces and the classical Fourier transform. Following this is a chapter covering the Paley-Wiener Theorem, distributions, convolution, the Sobolev Lemma, the Shannon Sampling Theorem, windowed and wavelet transforms, and the Poisson summation formula. The later chapters deal with non-commutative theory. Topics include abstract homogeneous spaces and fundamentals of representation theory. These are used in the last two chapters. The first covers the Heisenberg group which encode the Heisenberg uncertainty principle. This is first instance of the use of infinite dimensional representations. The last covers the basic theory of compact groups. Here finite dimensionality is sufficient. Spherical functions and Gelfand pairs are discussed. There is also a section on finite groups. The text is interspersed with over 50 exercise sets that range in difficulty from basic to challenging. The text should be useful to graduate students in mathematics, physics, and engineering.

Author : Anton Deitmar
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 51,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475738346

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A First Course in Harmonic Analysis by Anton Deitmar Pdf

This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes 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 final 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.

Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 49,7 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821815236

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Noncommutative Harmonic Analysis by Michael Eugene Taylor Pdf

This book explores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations. It began as lecture notes for a one-semester graduate course given by the author in noncommutative harmonic analysis. It is a valuable resource for both graduate students and faculty, and requires only a background with Fourier analysis and basic functional analysis, plus the first few chapters of a standard text on Lie groups. The basic method of noncommutative harmonic analysis, a generalization of Fourier analysis, is to synthesize operators on a space on which a Lie group has a unitary representation from operators on irreducible representation spaces.Though the general study is far from complete, this book covers a great deal of the progress that has been made on important classes of Lie groups. Unlike many other books on harmonic analysis, this book focuses on the relationship between harmonic analysis and partial differential equations. The author considers many classical PDEs, particularly boundary value problems for domains with simple shapes, that exhibit noncommutative groups of symmetries. Also, the book contains detailed work, which has not previously been published, on the harmonic analysis of the Heisenberg group and harmonic analysis on cones.

Author : J. Carmona,M. Vergne
Publisher : Unknown
Page : 560 pages
File Size : 52,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662176297

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Non Commutative Harmonic Analysis and Lie Groups by J. Carmona,M. Vergne Pdf

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217725

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Harmonic Analysis on the Heisenberg Group by Sundaram Thangavelu Pdf

The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.

Author : L. Auslander,R. Tolimieri
Publisher : Springer
Page : 104 pages
File Size : 43,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540374053

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Abelian Harmonic Analysis, Theta Functions and Functional Algebras on a Nilmanifold by L. Auslander,R. Tolimieri Pdf

Author : J. Carmona,J. Dixmier,M. Vergne
Publisher : Unknown
Page : 248 pages
File Size : 52,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662179741

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Non-Commutative Harmonic Analysis by J. Carmona,J. Dixmier,M. Vergne Pdf

Author : Gerald B. Folland
Publisher : CRC Press
Page : 292 pages
File Size : 54,5 Mb
Release : 1994-12-27
Category : Mathematics
ISBN : 0849384907

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A Course in Abstract Harmonic Analysis by Gerald B. Folland Pdf

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.

Author : Nolan R. Wallach
Publisher : Academic Press
Page : 439 pages
File Size : 54,7 Mb
Release : 1988-03-01
Category : Mathematics
ISBN : 9780080874517

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Real Reductive Groups I by Nolan R. Wallach Pdf

Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.

Author : James Glimm
Publisher : Unknown
Page : 120 pages
File Size : 54,8 Mb
Release : 1965
Category : Functions
ISBN : STANFORD:36105033241212

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Lectures on Harmonic Analysis (non-Abelian) by James Glimm Pdf

Author : Jorgensen Palle,Tian Feng
Publisher : World Scientific
Page : 564 pages
File Size : 49,5 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9789813202146

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Non-commutative Analysis by Jorgensen Palle,Tian Feng Pdf

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.) A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.