Progress in Mathematics

Harmonic Analysis on the Heisenberg Group

Editors: Thangavelu, Sundaram (Ed.)

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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.

Reviews

"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


Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4612-1772-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-0-8176-4050-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-1-4612-7275-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Harmonic Analysis on the Heisenberg Group
Editors
  • Sundaram Thangavelu
Series Title
Progress in Mathematics
Series Volume
159
Copyright
1998
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1772-5
DOI
10.1007/978-1-4612-1772-5
Hardcover ISBN
978-0-8176-4050-7
Softcover ISBN
978-1-4612-7275-5
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XII, 195
Topics