Non Abelian Harmonic Analysis
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Non Abelian Harmonic Analysis
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Author : Roger E. Howe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Abelian Harmonic Analysis written by Roger E. Howe 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.
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.
Non Abelian Harmonic Analysis
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Author : Roger Howe
language : en
Publisher:
Release Date : 1992-02-27
Non Abelian Harmonic Analysis written by Roger Howe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-27 with categories.
Non Commutative Harmonic Analysis
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Author : J. Carmona
language : en
Publisher: Springer
Release Date : 2006-11-15
Non Commutative Harmonic Analysis written by J. Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Non Commutative Harmonic Analysis
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Author : Raymond C. Fabec
language : en
Publisher:
Release Date : 2014-07-06
Non Commutative Harmonic Analysis written by Raymond C. Fabec and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-06 with Fourier analysis categories.
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.
Non Commutative Harmonic Analysis And Lie Groups
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Author : J. Carmona
language : en
Publisher:
Release Date : 2014-01-15
Non Commutative Harmonic Analysis And Lie Groups written by J. Carmona and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Non Commutative Harmonic Analysis
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Author : J. Carmona
language : en
Publisher:
Release Date : 2014-01-15
Non Commutative Harmonic Analysis written by J. Carmona and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Noncommutative Harmonic Analysis
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Author : Michael Eugene Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Noncommutative Harmonic Analysis written by Michael Eugene Taylor 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 1986 with Mathematics categories.
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.
Lectures On Harmonic Analysis Non Abelian
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Author : James Glimm
language : en
Publisher:
Release Date : 1965
Lectures On Harmonic Analysis Non Abelian written by James Glimm and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Functions categories.
Non Commutative Analysis
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Author : Jorgensen Palle
language : en
Publisher: World Scientific
Release Date : 2017-01-24
Non Commutative Analysis written by Jorgensen Palle and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
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.
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.