Convergence of finite dimensional distributions of heat kernel measures on loop groups

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Abstract

In this paper we consider heat kernel measure on loop groups associated to the H 1/2 -metric. Unlike H s -case (s > 1/2), there is a difficulty that H 1/2 is not contained in the space of continuous loops. So we take limits. There are two limiting methods. One is to use delta functions and to let s go down to 1/2. The other is to fix s at 1/2 and to approximate the delta functions. For the second approach, a generalization of heat kernel measures is needed. Then, the first approach can be obtained as a special case of the second one. The limit in the sense of finite dimensional distribution is the fictitious infinite dimensional Haar measure.

Original languageEnglish
Pages (from-to)311-340
Number of pages30
JournalJournal of Functional Analysis
Volume198
Issue number2
DOIs
Publication statusPublished - Mar 10 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

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