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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Editorial Board: Aldroubi, Akram / Anker, Jean-Philippe / Aouadi, Saloua / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Baraket, Sami / Ben Abdelghani, Leila / Begehr, Heinrich / Beznea, Lucian / Bezzarga, Mounir / Bonami, Aline / Demailly, Jean-Pierre / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jarboui, Noomen / Jouini, Elyes / Karoui, Abderrazek / Kamoun, Lotfi / Kobayashi, Toshiyuki / Maday, Yvon / Marzougui, Habib / Mili, Maher / Mustapha, Sami / Ovsienko, Valentin / Peigné, Marc / Pouzet, Maurice / Radulescu, Vicentiu / Schwartz, Lionel / Sifi, Mohamed / Zaag, Hatem / Zarati, Said

CiteScore 2017: 1.29

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

Suparna Sen
  • Corresponding author
  • 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
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Published Online: 2015-11-17 | DOI: https://doi.org/10.1515/apam-2015-0010


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

About the article

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.

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