The convolution equation of Choquet and Deny on [IN]-groups |
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Authors: | Cho-Ho Chu Chi-Wai Leung |
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Institution: | (1) Goldsmiths College, University of London, SE14 6NW London, England;(2) Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong |
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Abstract: | Let be a probability measure on a locally compact groupG. A real Borel functionf onG is called -harmonic if it satisfies the convolution equation *f=f. Given that isnonsingular with its translates, we show that the bounded -harmonic functions are constant on a class of groups including the almost connected IN]-groups. If is nondegenerate and absolutely continuous, we solve the more general equation *= for positive measure on those groups which are metrizable and separable.Supported by Hong Kong RGC Earmarked Grant and CUHK Direct Grant |
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Keywords: | 1991 Mathematics Subject Classification" target="_blank">1991 Mathematics Subject Classification 45E10 43A05 46A55 31C05 |
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