Brian C. Hall
Harmonic analysis with respect to heat kernel measure
(130K, Latex)

ABSTRACT.  I review certain results in harmonic analysis for system 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.