The Segal-Bargmann Transform on Compact Symmetric Spaces and their Direct Limits

Gestur Olafsson, Keng Wiboonton

We study the Segal-Bargmann transform, or the heat transform, $H_t$ for a compact symmetric space $M=U/K$. We prove that $H_t$ is a unitary isomorphism $H_t : L^2(M) \to \cH_t (M_\…