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