Integration by Parts and Quasi-Invariance for Heat Kernel Measures on Loop Groups
Integration by parts formulas are established both for 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 timet,t>0, dist...
Saved in:
| Published in | Journal of functional analysis Vol. 149; no. 2; pp. 470 - 547 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.10.1997
|
| Online Access | Get full text |
Cover
Loading…
| Summary: | Integration by parts formulas are established both for 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 timet,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 B. K. Driver and T. Lohrenz [1996,J. Functional Anal.140, 381–448]. We also show that the heat kernel measures are quasi-invariant under right under right and left translations by finite energy loops. |
|---|---|
| ISSN: | 0022-1236 1096-0783 |
| DOI: | 10.1006/jfan.1997.3103 |