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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convolution powers of singular-symmetric measures. II


Author: Keiji Izuchi
Journal: Proc. Amer. Math. Soc. 65 (1977), 313-317
MSC: Primary 43A05
DOI: https://doi.org/10.1090/S0002-9939-1977-0462441-3
MathSciNet review: 462441
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Abstract: Let G be an infinite compact abelian group such that its dual group contains an infinite independent subset. $ \mathfrak{L}(G)$ denotes the sum of all radicals of group algebras contained in the measure algebra on G. Then, for a positive integer k, there is a measure $ \mu $ on G such that $ {\mu ^n}$ is singular-symmetric for $ 1 \leqslant n \leqslant k$ and $ {\mu ^n} \in \mathfrak{L}(G)$ for $ n > k$.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0462441-3
Keywords: Convolution powers, singular-symmetric, measure algebra
Article copyright: © Copyright 1977 American Mathematical Society