Harmonic analysis on discrete Abelian groups

M. Laczkovich; G. Székelyhidi

doi:10.1090/S0002-9939-04-07749-4

Harmonic analysis on discrete Abelian groups

M. Laczkovich^*, G. Székelyhidi

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

Let G be an Abelian group and let 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 CG contains an exponential; that is, a nonzero multiplicative function. (ii) The torsion free rank of G is less than the continuum.

Original language	English (US)
Pages (from-to)	1581-1586
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	133
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-04-07749-4
State	Published - Jun 2005

Keywords

Exponential functions
Hilbert's Nullstellensatz
Problem of harmonic analysis

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-04-07749-4

Cite this

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abstract = "Let G be an Abelian group and let CG 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 CG 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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AU - Székelyhidi, G.

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N2 - Let G be an Abelian group and let CG 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 CG contains an exponential; that is, a nonzero multiplicative function. (ii) The torsion free rank of G is less than the continuum.

AB - Let G be an Abelian group and let CG 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 CG contains an exponential; that is, a nonzero multiplicative function. (ii) The torsion free rank of G is less than the continuum.

KW - Exponential functions

KW - Hilbert's Nullstellensatz

KW - Problem of harmonic analysis

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EP - 1586

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -

Harmonic analysis on discrete Abelian groups

Abstract

Keywords

ASJC Scopus subject areas

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