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Applicable Analysis
An International Journal
Volume 85, 2006 - Issue 8
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Original Articles

Positive definite temperature functions on the Heisenberg group

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Pages 987-1000 | Received 10 Oct 2006, Accepted 10 May 2006, Published online: 04 Sep 2006
 

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.

Acknowledgment

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

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