The convolution equation of Choquet and Deny on [IN]-groups
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AbstractLet sigma be a probability measure on a locally compact group G. A real Borel function f on G is called a-harmonic if it satisfies the convolution equation sigma * f = f. Given that sigma is nonsingular with its translates, we show that the bounded sigma -harmonic functions are constant on a class of groups including the almost connected [IN]-groups. If sigma is nondegenerate and absolutely continuous, we solve the more general equation sigma * mu = mu for positive measure mu on those groups which are metrizable and separable.
All Author(s) ListChu CH, Leung CW
Journal nameIntegral Equations and Operator Theory
Year2001
Month8
Day1
Volume Number40
Issue Number4
PublisherBIRKHAUSER VERLAG AG
Pages391 - 402
ISSN0378-620X
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2021-13-01 at 23:37