Harmonic Analysis on the Heisenberg Group

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Birkhauser, Jan 1, 1998 - Analyse harmonique - 191 pages
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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. 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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Contents

THE GROUP FOURIER TRANSFORM
1
ANALYSIS OF THE SUBLAPLACIAN
49
GROUP ALGEBRAS AND APPLICATIONS
109
THE REDUCED HEISENBERG GROUP
155
INDEX
192
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