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Harmonic Analysis on the Heisenberg Group

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 725/5 ( reviews)

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Book Synopsis Harmonic Analysis on the Heisenberg Group by : Sundaram Thangavelu

Download or read book Harmonic Analysis on the Heisenberg Group written by Sundaram Thangavelu. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Explorations in Harmonic Analysis

2009-05-24 Mathematics
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Release : 2009-05-24
Genre : Mathematics
Kind : eBook
Book Rating : 698/5 ( reviews)

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Book Synopsis Explorations in Harmonic Analysis by : Steven G. Krantz

Download or read book Explorations in Harmonic Analysis written by Steven G. Krantz. This book was released on 2009-05-24. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.

Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group

2009-06-13 Mathematics
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Release : 2009-06-13
Genre : Mathematics
Kind : eBook
Book Rating : 331/5 ( reviews)

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Book Synopsis Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group by : Valery V. Volchkov

Download or read book Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group written by Valery V. Volchkov. This book was released on 2009-06-13. Available in PDF, EPUB and Kindle. Book excerpt: The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active ?eld of investigation at 2 the moment. The simplest examples of symmetric spaces, the classical 2-sphere S 2 and the hyperbolic plane H , play familiar roles in many areas in mathematics. The n Heisenberg groupH is a principal model for nilpotent groups, and results obtained n forH may suggest results that hold more generally for this important class of Lie groups. The purpose of this book is to develop harmonic analysis of mean periodic functions on the above spaces.

Principles of Harmonic Analysis

2014-06-21 Mathematics
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Release : 2014-06-21
Genre : Mathematics
Kind : eBook
Book Rating : 928/5 ( reviews)

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Book Synopsis Principles of Harmonic Analysis by : Anton Deitmar

Download or read book Principles of Harmonic Analysis written by Anton Deitmar. This book was released on 2014-06-21. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Harmonic Analysis in Phase Space. (AM-122), Volume 122

2016-03-02 Mathematics
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Release : 2016-03-02
Genre : Mathematics
Kind : eBook
Book Rating : 427/5 ( reviews)

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Book Synopsis Harmonic Analysis in Phase Space. (AM-122), Volume 122 by : Gerald B. Folland

Download or read book Harmonic Analysis in Phase Space. (AM-122), Volume 122 written by Gerald B. Folland. This book was released on 2016-03-02. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

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