The Segal-Bargmann transform on a symmetric space of compact type

We study the Segal-Bargmann transform on a symmetric space X of compact type, mapping L-2(X) into holomorphic functions on the complexification X-C. We invert this transform by integrating against a "dual" heat kernel measure in the fibers of a natural fibration of X-C over X. We prove that the Segal-Bargmann transform is an isometry from L-2(X) Onto the space of holomorphic functions on X-C which are square integrable with respect to a natural measure. These results extend those of B. Hall in the compact group case. (C) 1999 Academic Press.