Harmonic functions on homogeneous spaces
Publication in refereed journal

香港中文大學研究人員

引用次數
替代計量分析
.

其它資訊
摘要Given a locally compact group G acting on a locally compact space X and a probability measure sigma on G, a real Borel function f on X is called sigma-harmonic if it satisfies the convolution equation f = sigma*f. We give conditions for the absence of nonconstant bounded harmonic functions. We show that, if G is a union of sigma-admissible neighbourhoods of the identity, relative to X, then every bounded sigma-harmonic function on X is constant. Consequently, for spread out sigma, the bounded sigma-harmonic functions are constant on each connected component of a [SIN]-group and, if G acts strictly transitively on a splittable metric space X, then the bounded sigma-harmonic functions on X are constant which extends Furstenberg's result for connected semisimple Lie groups.
著者Chu CH, Leung CW
期刊名稱Monatshefte für Mathematik
出版年份1999
月份1
日期1
卷號128
期次3
出版社SPRINGER-VERLAG WIEN
頁次227 - 235
國際標準期刊號0026-9255
電子國際標準期刊號1436-5081
語言英式英語
關鍵詞[SIN]-group; harmonic function; homogeneous space; Liouville property
Web of Science 學科類別Mathematics; MATHEMATICS

上次更新時間 2021-22-02 於 00:07