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Proceedings of the American Mathematical Society

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

 

 

Lipschitz functions and spectral synthesis


Author: Sung Yung Lee
Journal: Proc. Amer. Math. Soc. 83 (1981), 715-719
MSC: Primary 43A45; Secondary 42A65
DOI: https://doi.org/10.1090/S0002-9939-1981-0630043-2
MathSciNet review: 630043
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Abstract: An $ S$-set in the circle group $ T$ is a closed subset $ S$ of $ T$ for which $ \overline {j(S)} = k(S)$. We construct a non-$ S$-set $ S$ satisfying

$\displaystyle \bigcup\limits_{\alpha > 0} {{{\operatorname{Lip} }_\alpha }(T) \cap k(S) \subset \overline {j(S)} .} $

Thus $ {\operatorname{Lip} _\alpha }(T) \cap A(T)$ is not a big enough part of $ A(T)$ to test the synthesizability of a given closed subset of $ T$.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0630043-2
Keywords: Spe$ S$tral synthesis, $ S$-sets, Lipschitz function
Article copyright: © Copyright 1981 American Mathematical Society