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Harmonic analysis with respect to heat kernel measure

Brian C. Hall
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Abstract

I review certain results in harmonic analysis for systems whose configuration space is a compact Lie group. The results described involve a heat kernel measure, which plays the same role as a Gaussian measure on Euclidean space. The main constructions are group analogs of the Hermite expansion, the Segal-Bargmann transform, and the Taylor expansion. The results are related to geometric quantization, to stochastic analysis, and to the quantization of 1+1-dimensional Yang-Mills theory.

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Brian C. Hall. 2000-06-07. Harmonic analysis with respect to heat kernel measure. https://arxiv.org/abs/quant-ph/0006037

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