Harmonic Analysis On Heisenberg Nilmanifolds

Thangavelu, Sundaram (2009) Harmonic Analysis On Heisenberg Nilmanifolds. In: Revista De La Union Matematica Argentina, 50 (2). pp. 75-93.

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Abstract

In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Gamma<span class='textbac'>k</span>slash}H-n. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L-2 (Gamma<span class='textbac'>k</span>slash}H-n) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and characterise the image of L-2 (Gamma<span class='textbac'>k</span>slashH-n) in terms of twisted Bergman and Hermite Bergman spaces.

Item Type:	Journal Article
Additional Information:	Copyright for this article belongs to Union Matematica Argentina.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	27 Jan 2010 09:53
Last Modified:	19 Sep 2010 05:54
URI:	http://eprints.iisc.ernet.in/id/eprint/25453

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