A converse to Kluvánek’s theorem

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Publication details

JournalJournal of Fourier Analysis and Applications
DatePublished - Apr 2007
Issue number2
Volume13
Number of pages10
Pages (from-to)187-196
Original languageEnglish

Abstract

I. Kluvánek extended the Whittaker-Kotel’nikov-Shannon (WKS) theorem to the abstract harmonic analysis setting. To do this, the ‘band limited’ condition on the spectrum of a continuous square-integrable function (analogue signal) required for classical WKS theorem is replaced by an ‘almost disjoint’ translates condition arising from the Fourier transform of the function vanishing almost everywhere outside a transversal of a compact quotient group. A converse of Kluvánek’s theorem is established, i.e., if the representation given by the abstract WKS theorem holds for a continuous square-integrable function with support of its Fourier transform essentially A, then A is a subset of a transversals of Gamma/Lambda

    Research areas

  • Whittaker-Kotel'nikov-Shannon theorem, Plancherel's formula, locally compact abelian groups, discrete subgroups, transversals

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