Holomorphic Sobolev spaces associated to compact symmetric spaces

Using Gutzmer’s formula, due to Lassalle, we characterise the images of Sobolev spaces under the Segal– Bargmann transform on compact Riemannian symmetric spaces. We also obtain necessary and sufficient conditions on a holomorphic function to be in the image of smooth functions and distributions under the Segal–Bargmann transform. © 2007 Elsevier Inc. All rights reserved