Segal–Bargmann Transform and Paley–Wiener Theorems on Motion Groups

Sen, Suparna

doi:10.2977/PRIMS/23

Publications of the Research Institute for Mathematical Sciences

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Volume 46, Issue 3, 2010, pp. 719–740

DOI: 10.2977/PRIMS/23

Segal–Bargmann Transform and Paley–Wiener Theorems on Motion Groups

Suparna Sen (1)

(1) Department of Mathematics, Indian Institute of Science, 560 012, BANGALORE, INDIA

We study the Segal–Bargmann transform on a motion group ℝⁿ ⋉ K, where K is a compact subgroup of SO(n). A characterization of the Poisson integrals associated to the Laplacian on ℝⁿ ⋉ K is given. We also establish a Paley–Wiener type theorem using complexified representations.

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