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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Balayage by Fourier transforms with sparse frequencies in compact abelian torsion groups
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by George S. Shapiro PDF
Proc. Amer. Math. Soc. 71 (1978), 253-256 Request permission

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
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 253-256
  • MSC: Primary 43A25
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0493174-6
  • MathSciNet review: 0493174