The heat kernel transform for the Heisenberg group
arXiv:math/0401243
Abstract
The heat kernel transform H_t for the Heisenberg group is studied in detail. The main result shows that the image of H_t is a direct sum of two weighted Bergman spaces whose associated weighted functions are of oscillatory nature, i.e. attain positive and negative values.
26 pages, 1 figure.Extended final version. To appear in JFA. We would like to express our sincere gratitude to a referee who read the manuscript very carefully and pointed out several inaccuracies, gaps and mistakes