Harmonic functions on hypergroups

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• 作者：Massoud Amini^a ; ^b ; ¹ ; ^{mamini@modares.ac.ir"" rel=""nofollow} ; Cho-Ho Chu^c ; ^{c.chu@qmul.ac.uk"" rel=""nofollow}
• 关键词：Harmonic function ; Spherical function ; Nilpotent hypergroup ; Spherical hypergroup ; Liouville theorem ; Harnack inequality
• 刊名：Journal of Functional Analysis
• 出版年：2011
• 出版时间：1 October 2011
• 年：2011
• 卷：261
• 期：7
• 页码：1835-1864
• 全文大小：233 K

文摘

We initiate a study of harmonic functions on hypergroups. In particular, we introduce the concept of a nilpotent hypergroup and show such hypergroup admits an invariant measure as well as a Liouville theorem for bounded harmonic functions. Further, positive harmonic functions on nilpotent hypergroups are shown to be integrals of exponential functions. For arbitrary hypergroups, we derive a Harnack inequality for positive harmonic functions and prove a Liouville theorem for compact hypergroups. We discuss an application to harmonic spherical functions.