Integration by Parts and Quasi-Invariance for Heat Kernel Measures on Loop Groups
Integration by Parts and Quasi-Invariance for Heat Kernel Measures on Loop Groups
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DOI：
10.1006/jfan.1997.3103
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发表时间：
1997-10
影响因子：
1.7
通讯作者：
B. Driver
中科院分区：
文献类型：
--
作者：
B. Driver
摘要 建立了环群路径空间维纳测度和环群热核测度的分部积分公式。维纳测度被定义为特定循环群“布朗运动”的定律，热核测度是时间 t ，t >0，该布朗运动的分布。这些按部分公式进行积分的任何一个的推论是 B. K. Driver 和 T. Lohrenz 考虑的前狄利克雷形式的可封闭性 [1996，J.Functional Anal。 140, 381–448]。我们还表明，热核测量在有限能量循环的右下右下和平移下是准不变的。
Abstract Integration by parts formulas are established both for 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 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 B. K. Driver and T. Lohrenz [1996, J. Functional Anal. 140 , 381–448]. We also show that the heat kernel measures are quasi-invariant under right under right and left translations by finite energy loops.