The heat kernel transform for the Heisenberg group

摘要

The heat kernel transform H-1 is studied for the Heisenberg group in detail. The main result shows that the image of H-1, is a direct sum of two weighted Bergman spaces, in contrast to the classical case of R-n and compact symmetric spaces, and the weight functions are found to be (surprisingly) not non-negative. (c) 2005 Elsevier Inc. All rights reserved.