HYPOELLIPTIC HEAT KERNELS ON INFINITE-DIMENSIONAL HEISENBERG GROUPS

被引：6

作者：

Driver, Bruce K. ^{[1
]}

Eldredge, Nathaniel ^{[2
,3
]}

Melcher, Tai ^{[4
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

[3] Univ No Colorado, Sch Math Sci, Greeley, CO 80639 USA

[4] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 368卷 / 02期

基金：

美国国家科学基金会;

关键词：

Heisenberg group; hypoelliptic; heat kernel; smooth measures; QUASI-INVARIANCE;

D O I：

10.1090/tran/6461

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the law of a hypoelliptic Brownian motion on an infinite-dimensional Heisenberg group based on an abstract Wiener space. We show that the endpoint distribution, which can be seen as a heat kernel measure, is absolutely continuous with respect to a certain product of Gaussian and Lebesgue measures, that the heat kernel is quasi-invariant under translation by the Cameron-Martin subgroup, and that the Radon-Nikodym derivative is Malliavin smooth.

引用

页码：989 / 1022

页数：34

共 45 条

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