IBP and Quasi-Inv. on Loop Groups
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Integration by Parts and Quasi-Invariance for Heat Kernel Meausres on Loop Groups

(UCSD Preprint, December 30, 1996 )

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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.

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The manuscript is available as a DVI file (281K) or a Post Script file (565K).

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December 31, 1996

08/15/2016 02:53 PM