Monatshefte für Mathematik

, Volume 169, Issue 3–4, pp 267–284 | Cite as

Harmonic functions on [IN] and central hypergroups

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Abstract

In this paper we introduce the notions of [I N] and [S I N]-hypergroups and prove a Choquet-Deny type theorem for [I N] and central hypergroups. More precisely, we prove a Liouville theorem for bounded harmonic functions on a class of [I N]-hypergroups. Further, we show that positive harmonic functions on [I N]-hypergroups are integrals of exponential functions. Similar results are proved for [S I N] and central hypergroups.

Keywords

Convolution equation Harmonic function [IN]-hypergroup [SIN]-hypergroup Central hypergroup 

Mathematics Subject Classification

Primary 43A62 43A10 Secondary 45E10 31C05 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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