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

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4 Citations (Scopus)

### 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 language English 311-340 30 Journal of Functional Analysis 198 2 https://doi.org/10.1016/S0022-1236(02)00075-7 Published - Mar 10 2003 Yes

Loop Groups
Delta Function
Heat Kernel
Haar Measure
Limiting
Metric
Generalization

• Analysis

### Cite this

In: Journal of Functional Analysis, Vol. 198, No. 2, 10.03.2003, p. 311-340.

Research output: Contribution to journalArticle

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