Positive definite temperature functions on the Heisenberg group

Abstract

We characterize positive definite temperature functions, i.e., positive definite solutions of the heat equation, on the Heisenberg group in terms of the initial values. We also obtain an integral representation for positive definite and U(n)-invariant temperature functions with polynomial growth, where U(n) is the group of all n× n unitary matrices.

Keywords:

• Heisenberg group
• Sub-Laplacian
• Positive definite temperature functions

Keywords:

• 2000 Mathematics subject Classifications: Primary: 43A80
• Secondary: 35C15
• 35K05

Acknowledgment

This research has been supported by the Natural Sciences and Engineering Research Council of Canada.