We study the Segal–Bargmann transform on a motion group ℝ_n_ ⋉ K, where K is a compact subgroup of SO(n). A characterization of the Poisson integrals associated to the Laplacian on ℝ_n_ ⋉ K is given. We also establish a Paley–Wiener type theorem using complexified representations.
Cite this article
Suparna Sen, Segal–Bargmann Transform and Paley–Wiener Theorems on Motion Groups. Publ. Res. Inst. Math. Sci. 46 (2010), no. 3, pp. 719–740DOI 10.2977/PRIMS/23