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On the approximate form of Kluvánek's theorem

Research group:
Pure Mathematics
TitleOn the approximate form of Kluvánek's theorem
Publication TypeJournal Article
Year of Publication2009
AuthorsBeaty M, Dodson MM, Eveson S, Higgins JR
Refereed DesignationRefereed
JournalJournal of Approximation Theory
Volume160
Pagination281-303
AbstractAn 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 Kluv\'anek's theorem is established.
DOI10.1016/j.jat.2009.02.013

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Edited 28 Jun 2011 - 16:57 by spe1

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