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
Abstract:
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.References
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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: laczk@cs.elte.hu
- G. Székelyhidi
- Affiliation: Department of Mathematics, Imperial College, Huxley Building, 180 Queen’s Gate, London, SW7 2AZ, England
- MR Author ID: 754093
- Email: gabor.szekelyhidi@imperial.ac.uk
- 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: https://doi.org/10.1090/S0002-9939-04-07749-4
- MathSciNet review: 2120269