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

Authors

Suparna Sen, Indian Institute of Science

Article Type

Research Article

Publication Title

Advances in Pure and Applied Mathematics

Abstract

We consider the Heisenberg motion groups H = Hn K, 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 H and characterise the Poisson integrals associated to the Laplacian for H using Gutzmer's formula. We also prove a Paley-Wiener type theorem involving complexified representations using explicit realisations of some unitary irreducible representations of H.

First Page

13

Last Page

28

DOI

10.1515/apam-2015-0010

Publication Date

1-1-2016

Comments

Open Access; Bronze Open Access

Recommended Citation

Sen, Suparna, "Segal-Bargmann transform and Paley-Wiener theorems on Heisenberg motion groups" (2016). Journal Articles. 4433.
https://digitalcommons.isical.ac.in/journal-articles/4433