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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Harmonic analysis on discrete Abelian groups
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by M. Laczkovich and G. Székelyhidi PDF
Proc. Amer. Math. Soc. 133 (2005), 1581-1586 Request permission


Let $G$ be an Abelian group and let $\mathbb C^G$ denote the linear space of all complex-valued functions defined on $G$ equipped with the product topology. We prove that the following are equivalent. (i) Every nonzero translation invariant closed subspace of $\mathbb C^G$ contains an exponential; that is, a nonzero multiplicative function. (ii) The torsion free rank of $G$ is less than the continuum.
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Additional Information
  • M. Laczkovich
  • Affiliation: Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/C, 1117 Hungary – and – Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England
  • Email:
  • G. Székelyhidi
  • Affiliation: Department of Mathematics, Imperial College, Huxley Building, 180 Queen’s Gate, London, SW7 2AZ, England
  • MR Author ID: 754093
  • Email:
  • Received by editor(s): February 10, 2004
  • Published electronically: December 6, 2004
  • Additional Notes: The research of the first author was partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T032042
  • Communicated by: Andreas Seeger
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1581-1586
  • MSC (2000): Primary 20K99; Secondary 43A45, 12F05
  • DOI:
  • MathSciNet review: 2120269