Non Commutative Harmonic Analysis

Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : CRC Press
Page : 698 pages
File Size : 49,6 Mb
Release : 2000-09-28
Category : Computers
ISBN : 9781420041767

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Engineering Applications of Noncommutative Harmonic Analysis by Gregory S. Chirikjian,Alexander B. Kyatkin Pdf

The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is sti

Author : A.A. Kirillov
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 47,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662097564

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Representation Theory and Noncommutative Harmonic Analysis II by A.A. Kirillov Pdf

Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.

Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 42,7 Mb
Release : 1984
Category : Differential equations, Hypoelliptic
ISBN : 9780821823149

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Noncommutative Microlocal Analysis by Michael Eugene Taylor Pdf

Author : Jacques Carmona,Michèle Vergne
Publisher : Unknown
Page : 244 pages
File Size : 40,6 Mb
Release : 1979
Category : Electronic
ISBN : OCLC:872292796

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Non-Commutative Harmonic Analysis by Jacques Carmona,Michèle Vergne Pdf

Author : Nolan R. Wallach
Publisher : Academic Press
Page : 439 pages
File Size : 52,5 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 : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 46,6 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 : Jorgensen Palle,Tian Feng
Publisher : World Scientific
Page : 564 pages
File Size : 50,7 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.

Author : Anton Deitmar,Siegfried Echterhoff
Publisher : Springer
Page : 330 pages
File Size : 43,7 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 : Anton Deitmar
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 43,6 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 : J. Carmona,J. Dixmier,M. Vergne
Publisher : Springer
Page : 241 pages
File Size : 46,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540375241

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

Author : J. Carmona,M. Vergne
Publisher : Springer
Page : 562 pages
File Size : 49,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387831

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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 : 41,8 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 : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : CRC Press
Page : 555 pages
File Size : 51,5 Mb
Release : 2021-02-25
Category : Mathematics
ISBN : 9781000697339

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Engineering Applications of Noncommutative Harmonic Analysis by Gregory S. Chirikjian,Alexander B. Kyatkin Pdf

First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.

Author : Cho-Ho Chu,Anthony To-Ming Lau
Publisher : Springer
Page : 100 pages
File Size : 51,6 Mb
Release : 2004-10-11
Category : Mathematics
ISBN : 9783540477938

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Harmonic Functions on Groups and Fourier Algebras by Cho-Ho Chu,Anthony To-Ming Lau Pdf

This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.

Author : Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli
Publisher : Cambridge University Press
Page : 589 pages
File Size : 49,8 Mb
Release : 2018-06-21
Category : Mathematics
ISBN : 9781107182332

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Discrete Harmonic Analysis by Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli Pdf

A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.