© 1998

Harmonic Analysis on the Heisenberg Group


Part of the Progress in Mathematics book series (PM, volume 159)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Sundaram Thangavelu
    Pages 1-48
  3. Sundaram Thangavelu
    Pages 49-107
  4. Sundaram Thangavelu
    Pages 109-154
  5. Sundaram Thangavelu
    Pages 155-183
  6. Back Matter
    Pages 185-194

About this book


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.


Differential Geometry Fourier transform Gelfand pair Lie Quantum Physics Representation theory algebra calculus equation function geometry harmonic analysis mathematics theorem variable

Authors and affiliations

  1. 1.Statistics & Mathematics DivisionIndian Statistical InstituteBangaloreIndia

Bibliographic information

  • Book Title Harmonic Analysis on the Heisenberg Group
  • Editors Sundaram Thangavelu
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI
  • Copyright Information Birkhäuser 1998
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-4050-7
  • Softcover ISBN 978-1-4612-7275-5
  • eBook ISBN 978-1-4612-1772-5
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XII, 195
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Abstract Harmonic Analysis
    Group Theory and Generalizations
  • Buy this book on publisher's site


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