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
Full text not available from this repository.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 |
|---|---|
| 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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