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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0493174-6
PII: S 0002-9939(1978)0493174-6
Keywords: Balayage in Fourier transforms, arbitrarily sparse frequencies, compact abelian torsion group, approximation by characters
Article copyright: © Copyright 1978 American Mathematical Society