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Harmonic analysis on discrete Abelian groups |
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| Authors: | M Laczkovich G Szé kelyhidi |
| Institution: | 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 ; Department of Mathematics, Imperial College, Huxley Building, 180 Queen's Gate, London, SW7 2AZ, England |
| Abstract: | Let  be an Abelian group and let  denote the linear space of all complex-valued functions defined on  equipped with the product topology. We prove that the following are equivalent. (i) Every nonzero translation invariant closed subspace of (ii) The torsion free rank of |
| Keywords: | Problem of harmonic analysis exponential functions Hilbert's Nullstellensatz |
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contains an exponential; that is, a nonzero multiplicative function. 
is less than the continuum.