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A converse to Kluvánek’s theorem

Beaty, M.G., Dodson, M.M. and Eveson, S.P. (2007) A converse to Kluvánek’s theorem. Journal of Fourier Analysis and Applications, 13 (2). pp. 187-196. ISSN 1531-5851

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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 Γ/Λ

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 31 Jul 2009 13:59
Last Modified: 31 Jul 2009 13:59
Published Version: http://dx.doi.org/10.1007/s00041-006-6025-x
Status: Published
Publisher: Springer Science+Business Media
Identification Number: 10.1007/s00041-006-6025-x
URI: http://eprints.whiterose.ac.uk/id/eprint/6695

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