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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Helson Sets of Synthesis Are Ditkin Sets
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by Antony To-Ming Lau and Ali Ülger PDF
Proc. Amer. Math. Soc. 146 (2018), 2083-2090 Request permission

Abstract:

Let $G$ be a locally compact group and let $A(G)$ be its Fourier algebra. A closed subset $H$ of $G$ is said to be a Helson set if the restriction homomorphism $\phi :A(G)\rightarrow C_{0}(H)$, $\phi (a)=a_{|H}$, is surjective. In this paper, under the hypothesis that $G$ is amenable, we prove that every Helson subset $H$ of $G$ that is also a set of synthesis is a Ditkin set. This result is new even for $G=\mathbb {R}$.
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Additional Information
  • Antony To-Ming Lau
  • Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada T6G 2G1
  • MR Author ID: 110640
  • Email: antonyt@ualberta.ca
  • Ali Ülger
  • Affiliation: Department of Mathematics, Bogazici University, 34342 Bebek/Istanbul, Turkey
  • Email: aulger@ku.edu.tr
  • Received by editor(s): June 27, 2016
  • Received by editor(s) in revised form: July 10, 2017
  • Published electronically: December 11, 2017
  • Additional Notes: The first author was supported by NSERC grant ZC912
  • Communicated by: Thomas Schlumprecht
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 2083-2090
  • MSC (2010): Primary 43A46, 43A45, 42A63; Secondary 43A20
  • DOI: https://doi.org/10.1090/proc/13887
  • MathSciNet review: 3767359