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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Central Fourier-Stieltjes transforms with an isolated value

Author: Alan Armstrong
Journal: Trans. Amer. Math. Soc. 259 (1980), 423-437
MSC: Primary 43A10; Secondary 43A25
MathSciNet review: 567088
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Abstract: Let $\mu$ be a central Borel measure on a compact, connected group G. If 0 is isolated in the range of ${\hat \mu }$, then there exists a closed, normal subgroup H of G such that ${\pi _H}\mu$, the restriction of $\mu$ to the cosets of H, is the convolution of an invertible measure with a nonzero idempotent measure. This result extends I. Glicksberg’s result for LCA groups. An example is given which shows that this result is false in general for disconnected groups.

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Keywords: Central measure, Fourier-Stieltjes transform, isolated value
Article copyright: © Copyright 1980 American Mathematical Society