On subsets with associated compacta in discrete abelian groups
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- by Ron C. Blei PDF
- Proc. Amer. Math. Soc. 37 (1973), 453-455 Request permission
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 \[ \sup \limits _{x \in K} |p(x)| \geqq (1 - \varepsilon ){\left \| p \right \|_\infty },\quad {\text {for}}\;{\text {all}}\;p \in {C_{E\backslash \Lambda }}(\hat \Gamma ).\]References
- Ron C. Blei, On trigonometric series associated with separable, translation invariant subspaces of $L^{\infty }(G)$, Trans. Amer. Math. Soc. 173 (1972), 491–499. MR 313715, DOI 10.1090/S0002-9947-1972-0313715-8 M. Déchamps-Gondim, Compacts associés à un ensemble de Sidon, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A590-A592. MR 42 #6526.
- Myriam Déchamps-Gondim, Ensembles de Sidon topologiques, Ann. Inst. Fourier (Grenoble) 22 (1972), no. 3, 51–79 (French, with English summary). MR 340981
- Jean-François Méla, Sur certains ensembles exceptionnels en analyse de Fourier, Ann. Inst. Fourier (Grenoble) 18 (1968), no. 2, 31–71 (1969) (French). MR 412739
- Kenneth A. Ross, Fatou-Zygmund sets, Proc. Cambridge Philos. Soc. 73 (1973), 57–65. MR 310553, DOI 10.1017/s0305004100047460
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 453-455
- MSC: Primary 43A46
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313720-8
- MathSciNet review: 0313720