文献类型：期刊文献

英文题名：ON THE CYLINDRICAL GREEN'S FUNCTION FOR REPRESENTATION THEORY AND ITS APPLICATIONS

作者：Qiao, Lei[1]

第一作者：乔蕾

通讯作者：Qiao, L[1]

机构：[1]Henan Univ Econ & Law, Sch Math & Informat Sci, Zhengzhou 450046, Henan, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Henan Univ Econ & Law, Sch Math & Informat Sci, Zhengzhou 450046, Henan, Peoples R China.|[1048425]河南财经政法大学数学与信息科学学院;[10484]河南财经政法大学;

年份：2019

卷号：44

起止页码：1191-1206

外文期刊名：ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA

收录：;Scopus(收录号：2-s2.0-85106782384);WOS:【SCI-EXPANDED(收录号:WOS:000471244500034)】；

语种：英文

外文关键词：Cylindrical Green's function; cylindrical Green's potential; representation theory; covering property

摘要：It has been known for some time that the Green's function of a planar domain can be defined in terms of the exit time of Brownian motion, and this definition has been applied to the representation theory. In this paper, we extend the notion of conformal invariance of Green's function to superharmonic functions, and use this extension to construct and estimate the cylindrical Green's function for Dirichlet boundary value problem. These considerations lead to a new proof of the representation theory of superharmonic functions defined in cylinders. We also show this estimation can be used to obtain a covering property of rarefied sets at infinity. Finally, by giving an example, we show that the reverse of this property is not true.