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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On subsets with associated compacta in discrete abelian groups

Author: Ron C. Blei
Journal: Proc. Amer. Math. Soc. 37 (1973), 453-455
MSC: Primary 43A46
MathSciNet review: 0313720
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Abstract: Let $ \Gamma $ be a discrete abelian group. We prove that every non-Sidon set in $ \Gamma $ contains F, a non-Sidon set with the property that for every $ \varepsilon > 0$ and compact set $ K \subset \hat \Gamma $ with nonempty interior, there exists a finite set $ \Lambda (\varepsilon ,K) \subset F$, so that

$\displaystyle \mathop {\sup }\limits_{x \in K} \vert p(x)\vert \geqq (1 - \vare... ...uad {\text{for}}\;{\text{all}}\;p \in {C_{E\backslash \Lambda }}(\hat \Gamma ).$

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PII: S 0002-9939(1973)0313720-8
Keywords: Sidon set
Article copyright: © Copyright 1973 American Mathematical Society