Harmonic Analysis on the Heisenberg Group

Overview

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 theorem, and its relations to classical special functions is invaluable for any reader interested in this group. Topics ...
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Hardcover (1998)
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Overview

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 theorem, and its relations to classical special functions is invaluable for any reader interested in this group. Topics 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.
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Editorial Reviews

From the Publisher

"The author is to be commended for assembling this diverse body of interesting results into a coherent and readable monograph…Thangavelu’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..."

–Mathematical Reviews

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Product Details

  • ISBN-13: 9780817640507
  • Publisher: Birkhauser Verlag
  • Publication date: 3/24/1998
  • Series: Progress in Mathematics Series , #159
  • Edition description: 1998
  • Edition number: 1
  • Pages: 195
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.50 (d)

Table of Contents

1 The Group Fourier Transform 1
2 Analysis of the Sublaplacian 49
3 Group Algebras and Applications 109
4 The Reduced Heisenberg Group 155
Index 192
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