Harmonic analysis with respect to heat kernel measure

Hall, Brian

doi:10.1090/S0273-0979-00-00886-7

Harmonic analysis with respect to heat kernel measure
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Bull. Amer. Math. Soc. 38 (2001), 43-78 Request permission

Abstract:

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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