Heat kernel transform on nilmanifolds associated to H-type groups

TL;DR

This paper investigates the heat kernel transform on nilmanifolds linked to H-type groups, reducing the problem to Heisenberg groups and characterizing the image as a sum of weighted Bergman spaces.

Contribution

It introduces a reduction technique for analyzing the heat kernel transform on H-type group nilmanifolds and describes its image explicitly.

Findings

The heat kernel transform's image is a direct sum of weighted Bergman spaces.

Reduction to Heisenberg groups simplifies the analysis.

Provides a structural understanding of the transform on nilmanifolds.

Abstract

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