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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

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1869-6090
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Segal–Bargmann transform and Paley–Wiener theorems on Heisenberg motion groups

Suparna Sen
  • Department of Mathematics, Indian Institute of Science, Bangalore 560012, India. Current address: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
  • :
Published Online: 2015-11-17 | DOI: https://doi.org/10.1515/apam-2015-0010

Abstract

We consider the Heisenberg motion groups ℍ𝕄 = ℍnK, where ℍn is the Heisenberg group and K is a compact subgroup of U(n) such that (K,ℍn) is a Gelfand pair. We study the Segal–Bargmann transform on ℍ𝕄 and characterise the Poisson integrals associated to the Laplacian for ℍ𝕄 using Gutzmer's formula. We also prove a Paley–Wiener type theorem involving complexified representations using explicit realisations of some unitary irreducible representations of ℍ𝕄.

Keywords: Segal–Bargmann transform; Poisson integrals; Paley–Wiener theorems

MSC: 22E30; 22E45


Received: 2015-02-24

Accepted: 2015-10-04

Published Online: 2015-11-17

Published in Print: 2016-01-01


Funding Source: Council of Scientific and Industrial Research, India

Award identifier / Grant number: Shyama Prasad Mukherjee Fellowship


Citation Information: Advances in Pure and Applied Mathematics. Volume 7, Issue 1, Pages 13–28, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2015-0010, November 2015

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