The image of the heat kernel transform on Riemannian symmetric spaces of the noncompact type

Abstract

The heat kernel or Bargmann-Segal transform on a noncompact Riemannian symmetric space X=G/K maps a square integrable function on X to a holomorphic function on the complex crown. In this article we determine the range of this transform.

Expanded version. Two new sections added in order to clarify two remarks in the previous verson. 15 p