CENTRAL GAUSSIAN CONVOLUTION SEMIGROUPS ON COMPACT GROUPS: A SURVEY
CENTRAL GAUSSIAN CONVOLUTION SEMIGROUPS ON COMPACT GROUPS: A SURVEY
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紧群上的中心高斯卷积半群：一项调查
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
L. SALOFF
中科院分区：
文献类型：
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作者：
A. Bendikov;L. SALOFF
这是一篇关于紧连通群上的布朗运动和相关高斯卷积半群的综述文章。重点讨论了无限维群，如无限维环面和特殊正交群的无限乘积。本文讨论了具有良好性质的布朗运动的存在性，如关于Haar测度具有连续密度的边值问题。我们将这些布朗运动的存在性与群的代数结构联系起来。我们所描述的结果一方面反映了无穷维的影响，另一方面反映了基础群的紧致性。
This is a survey article on Brownian motions on compact connected groups and the associated Gaussian convolution semigroups. The emphasize is on innite dimensional groups such as the innite dimensional torus and innite products of special orthogonal groups. We discuss the existence of Brownian motions having nice properties such as marginales having a continuous density with respect to Haar measure. We relate the existence of these Brownian motions to the algebraic structure of the group. The results we describe reect the conicting eects of, on the one hand, the innite dimensionality and, on the other hand, the compact nature of the underlying group.