EAN: 9781461272755

HARMONIC ANALYSIS ON THE HEISENBERG GROUP KARTO...

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.

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