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arXiv · 1008.2577

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

Suparna Sen
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Abstract

We study the Segal-Bargmann transform on the Heisenberg motion groups $\mathbb{H}^n \ltimes K,$ where $\mathbb{H}^n$ is the Heisenberg group and $K$ is a compact subgroup of $U(n)$ such that $(K,\mathbb{H}^n)$ is a Gelfand pair. The Poisson integrals associated to the Laplacian for the Heisenberg motion group are also characterized using Gutzmer's formulae. Explicitly realizing certain unitary irreducible representations of $\mathbb{H}^n \ltimes K,$ we prove the Plancherel theorem. A Paley-Wiener type theorem is proved using complexified representations.

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Suparna Sen. 2010-08-16. Segal-Bargmann transform and Paley-Wiener theorems on Heisenberg motion groups. https://arxiv.org/abs/1008.2577

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