### 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 |
---|---|

Pages (from-to) | 311-340 |

Number of pages | 30 |

Journal | Journal of Functional Analysis |

Volume | 198 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 10 2003 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Analysis

### Cite this

**Convergence of finite dimensional distributions of heat kernel measures on loop groups.** / Inahama, Yuzuru.

Research output: Contribution to journal › Article

*Journal of Functional Analysis*, vol. 198, no. 2, pp. 311-340. https://doi.org/10.1016/S0022-1236(02)00075-7

}

TY - JOUR

T1 - Convergence of finite dimensional distributions of heat kernel measures on loop groups

AU - Inahama, Yuzuru

PY - 2003/3/10

Y1 - 2003/3/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037430072&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037430072&partnerID=8YFLogxK

U2 - 10.1016/S0022-1236(02)00075-7

DO - 10.1016/S0022-1236(02)00075-7

M3 - Article

AN - SCOPUS:0037430072

VL - 198

SP - 311

EP - 340

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -