On the approximate form of Kluvánek's theorem

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JournalJournal of Approximation Theory
DatePublished - Sep 2009
Issue number1-2
Volume160
Number of pages23
Pages (from-to)281-303
Original languageEnglish

Abstract

An abstract form of the classical approximate sampling theorem is proved for functions on a locally compact abelian group that are continuous, square-integrable and have integrable Fourier transforms. An additional hypothesis that the samples of the function are square-summable is needed to ensure the convergence of the sampling series. As well as establishing the representation of the function as a sampling series plus a remainder term, an asymptotic formula is obtained under mild additional restrictions on the group. In conclusion a converse to Kluvánek's theorem is established.

    Research areas

  • Analysis, , Pure Mathematics

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