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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0567088-0
PII: S 0002-9947(1980)0567088-0
Keywords: Central measure, Fourier-Stieltjes transform, isolated value
Article copyright: © Copyright 1980 American Mathematical Society