Publications of the Research Institute for Mathematical Sciences
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Segal–Bargmann Transform and Paley–Wiener Theorems on Motion GroupsSuparna Sen
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
Sen S. Segal–Bargmann Transform and Paley–Wiener Theorems on Motion Groups. Publ. Res. Inst. Math. Sci. 46 (2010), 719-740. doi: 10.2977/PRIMS/23