Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



A characterization of $\textrm {SH}$-sets

Author: Sadahiro Saeki
Journal: Proc. Amer. Math. Soc. 30 (1971), 497-503
MSC: Primary 42.58
MathSciNet review: 0283500
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42.58

Retrieve articles in all journals with MSC: 42.58

Additional Information

Keywords: Locally compact abelian group, Helson set, <I>S</I>-set, <I>SH</I>-set, quasi-Kronecker set, <IMG WIDTH="32" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${K_p}$">-set, character, pseudomeasure
Article copyright: © Copyright 1971 American Mathematical Society