On a Class of Hungarian Semigroups and the Factorization Theorem of Khinchin |
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Authors: | C Robinson Edward Raja |
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Institution: | (1) Present address: Départment de Mathematiques, Université d'Angers, 2 blv. Lavoisier, 49045 Angers, France;(2) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400 005, India |
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Abstract: | Let G be a connected reductive Lie group and K be a maximal compact subgroup of G. We prove that the semigroup of all K-biinvariant probability measures on G is a strongly stable Hungarian semigroup. Combining with the result see Rusza and Szekely(9)], we get that the factorization theorem of Khinchin holds for the aforementioned semigroup. We also prove that certain subsemigroups of K-biinvariant measures on G are Hungarian semigroups when G is a connected Lie group such that Ad G is almost algebraic and K is a maximal compact subgroup of G. We also prove a p-adic analogue of these results. |
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Keywords: | Reductive Lie groups Hungarian semigroup K-invariant measures |
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