A characterization of $\textrm {SH}$-sets
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- by Sadahiro Saeki PDF
- Proc. Amer. Math. Soc. 30 (1971), 497-503 Request permission
Abstract:
Let G be a locally compact abelian group, and $A(G)$ the Fourier algebra on G. A Helson set in G is called an SH-set if it is also an S-set for the algebra $A(G)$. In this article we prove that a compact subset K of G is an SH-set if and only if there exists a positive constant b such that: For any disjoint closed subsets ${K_0}$ and ${K_1}$ of K, we can find a function u in $A(G)$ such that $\left \| u \right \| < b,u = 1$ on some neighborhood of ${K_0}$, and $u = 0$ on some neighborhood of ${K_1}$.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 497-503
- MSC: Primary 42.58
- DOI: https://doi.org/10.1090/S0002-9939-1971-0283500-9
- MathSciNet review: 0283500