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Transactions of the American Mathematical Society

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

 

 

Some thin sets in discrete abelian groups


Author: Ron C. Blei
Journal: Trans. Amer. Math. Soc. 193 (1974), 55-65
MSC: Primary 43A46
MathSciNet review: 0340980
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Abstract: Let $ \Gamma $ be a discrete abelian group, and $ E \subset \Gamma $. For $ F \subset E$, we say that $ F \in \mathcal{P}(E)$, if for all $ \Lambda $, finite subsets of $ \Gamma ,0 \notin \Lambda ,\Lambda + F \cap F$ is finite. Having defined the Banach algebra, $ \tilde A(E) = c(E) \cap B(E)$, we prove the following: (i) $ E \subset \Gamma $ is a Sidon set if and only if every $ F \in \mathcal{P}(E)$ is a Sidon set; (ii) $ E \in \mathcal{P}(\Gamma )$ is a Sidon set if and only if $ \tilde A(E) = A(E)$.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0340980-5
Keywords: Sidon set, infinite pace
Article copyright: © Copyright 1974 American Mathematical Society