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Harmonic Analysis on the Heisenberg Group by Sundaram Thangavelu

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Published by Birkhäuser Boston, Imprint: Birkhäuser in Boston, MA .
Written in English

Subjects:

  • Group theory,
  • Mathematics,
  • Harmonic analysis

Book details:

About the Edition

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. Several results in this monograph appear for the first time in book form, and some theorems have not appeared elsewhere. The detailed discussion of the representation theory of the Heisenberg group goes well beyond the basic Stone-von Neumann theory, and its relations to classical special functions is invaluable for any reader interested in this group. Topic covered include the Plancherel and Paley-Wiener theorems, spectral theory of the sublaplacian, Wiener-Tauberian theorems, Bochner-Riesz means and multipliers for the Fourier transform. 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.

Edition Notes

Statementby Sundaram Thangavelu
SeriesProgress in Mathematics -- 159, Progress in Mathematics -- 159
Classifications
LC ClassificationsQA403-403.3
The Physical Object
Format[electronic resource] /
Pagination1 online resource (xii, 195 p.)
Number of Pages195
ID Numbers
Open LibraryOL27043004M
ISBN 101461272750, 1461217725
ISBN 109781461272755, 9781461217725
OCLC/WorldCa853258467

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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. Several results in this monograph appear for the first time in book form, and some theorems have not appeared elsewhere. Get this from a library! Harmonic analysis on the Heisenberg group. [Sundaram Thangavelu] -- 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. Several results in this monograph appear for. 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 . 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. Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and Poisson–Szegö integrals on the Brand: Birkhäuser Basel.

1 The Group Fourier Transform.- The Heisenberg group.- The Schroedinger representations.- The Fourier and Weyl transforms.- Hermite and special Hermite functions.- Paley-Wiener theorems for the Fourier transform.- An uncertainty principle on the Heisenberg group.- Notes and references.- 2 Analysis of the Sublaplacian. Harmonic Analysis On The Heisenberg Group pdf. Harmonic Analysis On The Heisenberg Group pdf: Pages By Sundaram Thangavelu 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 book presents the first systematic and unified treatment of the theory of mean periodic functions on homogeneous spaces. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to harmonic analysis, complex analysis, integral geometry, and analysis on symmetric spaces. 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.

  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 Author: Sundaram Thangavelu. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The 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 /5. Book Description: This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on. 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.