Heat kernel analysis on semi-infinite Lie groups

Abstract

This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the $L^p$ norms of the Radon-Nikodym derivatives. We also prove that a logarithmic Sobolev inequality holds in this setting.

35 pages

References in corpus (1)

• Integrated Harnack inequalities on Lie groups