Overview

The Heisenberg group has been implicitly present in much of mathematics and physics for a long time. Thangavelu's work is developed within the framework of harmonic analysis (Fourier transforms, convolution algebra, and related ideas) and gives a survey of the field. Additionally the author discusses in detail the representation theory of the group and its relationship to the theory of classical special functions. Among the topics covered are the Plancherel and Paley-Wiener theorems, spectral theory of the sublaplacian, Wiener-Tauberian theorems, Bocher-Riesz means and multipliers for the Fourier transform. The exposition is systematic, and leads to several problems and conjectures for further consideration. Any reader who is interested in pursuing research on the Heisenberg group should find this text of use.

Full Product Details

Author:   Sundaram Thangavelu
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   1998 ed.
Volume:   159
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   1.050kg
ISBN:  

9780817640507

ISBN 10:   0817640509
Pages:   195
Publication Date:   24 March 1998
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 The Group Fourier Transform.- 1.1 The Heisenberg group.- 1.2 The Schrödinger representations.- 1.3 The Fourier and Weyl transforms.- 1.4 Hermite and special Hermite functions.- 1.5 Paley—Wiener theorems for the Fourier transform.- 1.6 An uncertainty principle on the Heisenberg group.- 1.7 Notes and references.- 2 Analysis of the Sublaplacian.- 2.1 Spectral theory of the sublaplacian.- 2.2 Spectral decomposition for Lp functions.- 2.3 Restriction theorems for the spectral projections.- 2.4 A Paley-Wiener theorem for the spectral projections.- 2.5 Bochner-Riesz means for the sublaplacian.- 2.6 A multiplier theorem for the Fourier transform.- 2.7 Notes and references.- 3 Group Algebras and Applications.- 3.1 The Heisenberg motion group.- 3.2 Gelfand pairs, spherical functions and group algebras.- 3.3 An algebra of radial measures.- 3.4 Analogues of Wiener-Tauberian theorem.- 3.5 Spherical means on the Heisenberg group.- 3.6 A maximal theorem for spherical means.- 3.7 Notes and references.- 4 The Reduced Heisenberg Group.- 4.1 The reduced Heisenberg group.- 4.2 A Wiener-Tauberian theorem for Lp functions.- 4.3 A maximal theorem for spherical means.- 4.4 Mean periodic functions on phase space.- 4.5 Notes and references.

Reviews

The author is to be commended for assembling this diverse body of interesting results into a coherent and readable monographa ]Thangavelua (TM)s work....gives a useful survey of the field, bringing together a number of recent results which have not appeared elsewhere in book form and which will appeal to a broad mathematical audience... <p>a Mathematical Reviews

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