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 1531-5851Full text not available from this repository.
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
|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|
|Publisher:||Springer Science+Business Media|