Leonard Gross's work in infinite-dimensional analysis and heat kernel analysis

This paper describes a certain part of Leonard Gross's work in infinite-dimensional analysis, connected to the Gross Ergodicity Theorem. I then look at way in which Gross's work helped to create a new subject within (mostly) finite-dimensional analysis, a subject which may be called "harmonic analysis with respect to heat kernel measure." This subject transfers to Lie groups certain constructions on R n that involves a Gaussian measure. On the Lie group, the role of the Gaussian measure is played by a heat kernel