Harmonic Analysis On The Heisenberg Group

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 47,9 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 : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 40,6 Mb
Release : 2009-05-24
Category : Mathematics
ISBN : 9780817646691

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Explorations in Harmonic Analysis by Steven G. Krantz Pdf

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.

Author : Valery V. Volchkov,Vitaly V. Volchkov
Publisher : Springer
Page : 0 pages
File Size : 41,9 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 1447122836

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Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group by Valery V. Volchkov,Vitaly V. Volchkov Pdf

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.

Author : Gerald B. Folland
Publisher : Princeton University Press
Page : 288 pages
File Size : 48,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882427

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

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.

Author : Anton Deitmar,Siegfried Echterhoff
Publisher : Springer
Page : 330 pages
File Size : 41,9 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 : 44,9 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 : Walter Schempp
Publisher : Longman Publishing Group
Page : 220 pages
File Size : 40,7 Mb
Release : 1986
Category : Harmonic analysis
ISBN : UCAL:B4405819

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Harmonic Analysis on the Heisenberg Nilpotent Lie Group, with Applications to Signal Theory by Walter Schempp Pdf

Author : Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli
Publisher : Cambridge University Press
Page : 589 pages
File Size : 40,7 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.

Author : Joseph Albert Wolf
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 54,8 Mb
Release : 2007
Category : Abelian groups
ISBN : 9780821842898

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Harmonic Analysis on Commutative Spaces by Joseph Albert Wolf Pdf

This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.

Author : G. B. Folland
Publisher : Princeton University Press
Page : 288 pages
File Size : 55,8 Mb
Release : 1989-03-21
Category : Mathematics
ISBN : 9780691085289

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Harmonic Analysis in Phase Space by G. B. Folland Pdf

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.

Author : Valery V. Volchkov,Vitaly V. Volchkov
Publisher : Springer Science & Business Media
Page : 667 pages
File Size : 53,8 Mb
Release : 2009-06-13
Category : Mathematics
ISBN : 9781848825338

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Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group by Valery V. Volchkov,Vitaly V. Volchkov Pdf

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.

Author : Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate
Publisher : Birkhäuser
Page : 256 pages
File Size : 40,7 Mb
Release : 2015-09-12
Category : Mathematics
ISBN : 9783319188638

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Harmonic and Applied Analysis by Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate Pdf

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.​

Author : Ernst Binz,Sonja Pods
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 44,9 Mb
Release : 2008
Category : Heisenberg uncertainty principle
ISBN : 9780821844953

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The Geometry of Heisenberg Groups by Ernst Binz,Sonja Pods Pdf

"The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.

Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 55,8 Mb
Release : 1984
Category : Differential equations, Hypoelliptic
ISBN : 9780821823149

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Noncommutative Microlocal Analysis by Michael Eugene Taylor Pdf

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681647

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An Introduction to the Uncertainty Principle by Sundaram Thangavelu Pdf

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.