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Proceedings of the American Mathematical Society

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



Balayage by Fourier transforms with sparse frequencies in compact abelian torsion groups

Author: George S. Shapiro
Journal: Proc. Amer. Math. Soc. 71 (1978), 253-256
MSC: Primary 43A25
MathSciNet review: 0493174
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Abstract: Let $\Lambda$ be a discrete subset of a LCA group and E a compact subset of the dual group $\Gamma$. Balayage is said to be possible for ($\Lambda$, E) if the Fourier transform of each measure on G is equal on E to the Fourier transform of some measure supported by $\Lambda$. For a class of infinite compact metrizable $\Gamma$, including all such torsion groups, we show how to construct $E \subset \Gamma$ such that there are arbitrarily sparse sets $\Lambda$ with balayage possible for ($\Lambda$, E). E is, moreover, large enough that the set of products $E \cdot E \cdot E = \Gamma$.

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Keywords: Balayage in Fourier transforms, arbitrarily sparse frequencies, compact abelian torsion group, approximation by characters
Article copyright: © Copyright 1978 American Mathematical Society