Heat kernel transform for nilmanifolds associated to the Heisenberg group

Abstract

We study the heat kernel transform on a nilmanifold $ M $ of the Heisenberg group. We show that the image of $ L^2(M) $ under this transform is a direct sum of weighted Bergman spaces which are related to twisted Bergman and Hermite-Bergman spaces.

Revised version; to appear in Revista Mathematica Iberoamericana, 28 p