Harmonic analysis on discrete Abelian groups

M. Laczkovich*, G. Székelyhidi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1581-1586
Number of pages6
JournalProceedings of the American Mathematical Society
Volume133
Issue number6
DOIs
StatePublished - Jun 2005

Keywords

  • Exponential functions
  • Hilbert's Nullstellensatz
  • Problem of harmonic analysis

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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