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Harmonic analysis with respect to heat kernel measure

Author: Brian C. Hall
Journal: Bull. Amer. Math. Soc. 38 (2001), 43-78
MSC (2000): Primary 22E30, 81S30, 53D50, 60H30; Secondary 43A32, 46E20, 58J25
Published electronically: September 26, 2000
MathSciNet review: 1803077
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This paper surveys developments over the last decade in harmonic analysis on Lie groups relative to a heat kernel measure. These include analogs of the Hermite expansion, the Segal-Bargmann transform, and the Taylor expansion. Some of the results can be understood from the standpoint of geometric quantization. Others are intimately related to stochastic analysis.

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Additional Information

Brian C. Hall
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Received by editor(s): June 7, 2000
Published electronically: September 26, 2000
Article copyright: © Copyright 2000 American Mathematical Society