The heat kernel transform for the Heisenberg group

The heat kernel transform Ht is studied for the Heisenberg group in detail. The main result shows that the image of Ht is a direct sum of two weighted Bergman spaces, in contrast to the classical case of Rn and compact symmetric spaces, and the weight functions are found to be (surprisingly) not non-negative. © 2005 Elsevier Inc. All rights reserved.