Convergence of finite dimensional distributions of heat kernel measures on loop groups
Convergence of finite dimensional distributions of heat kernel measures on loop groups
复制标题
循环群上热核测度的有限维分布的收敛性
DOI：
10.1016/s0022-1236(02)00075-7
复制
发表时间：
2003
影响因子：
1.7
通讯作者：
Y. Inahama
中科院分区：
文献类型：
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作者：
Y. Inahama
本文考虑了与H_（1/2）-度量相关的圈群上的热核测度。与Hs-case（s>1/2）不同，H1/2不包含在连续环空间中是一个困难。所以我们要有限度。有两种限制方法。一个是使用delta函数，让s下降到1/2。另一种是将s固定在1/2，并近似δ函数。对于第二种方法，需要推广热核测度。然后，第一种方法可以作为第二种方法的特殊情况得到。有限维分布意义下的极限是虚拟的无限维Haar测度。
In this paper we consider heat kernel measure on loop groups associated to the H1/2-metric. Unlike Hs-case (s>1/2), there is a difficulty that H1/2is 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.