**Integration by Parts and Quasi-Invariance for Heat
Kernel Meausres on Loop Groups**
(UCSD Preprint, December 30, 1996* *)
Integration by parts formulas are established for both Wiener measure
on the path space of a loop group and for the heat kernel measures on the
loop group. The Wiener measure is defined to be the law of a certain loop
group valued ``Brownian motion'' and the heat kernel measures are the time
$t,$ $t>0,$ distributions of this Brownian motion. A corollary of either
of these integrations by parts formulas is the closability of the pre-Dirichlet
form considered by Driver and Lohrenz \cite{DL}. We also show that the
heat kernel measures are quasi-invariant under right and left translations
by finite energy loops.
The manuscript is available as a DVI
file (281K) or a Post
Script file (565K).
*December 31, 1996* |