HEAT KERNEL TRANSFORM ON NILMANIFOLDS ASSOCIATED TO H-TYPE GROUPS

Abstract

We study the heat kernel transform on a nilmanifold $\Gamma \backslash N$ associated to an H-type group. Using a reduction technique we reduce the problem to the case of Heisenberg groups. The image of $L^2(\Gamma \backslash N)$ under the heat kernel transform is shown to be a direct sum of weighted Bergman spaces.