Heat kernel analysis on semi-infinite Lie groups

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 Lp norms of the Radon–Nikodym derivatives. We also prove that a logarithmic Sobolev inequality holds in this setting. © 2009 Elsevier Inc. All rights reserved