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
Volume Number40
Issue Number4
Pages391 - 402
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesMathematics; MATHEMATICS

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