caa a22 4500 463247078 CHVBK 20180405153329.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s00041-006-6025-x doi (NATIONALLICENCE)springer-10.1007/s00041-006-6025-x A Converse to Kluvánek's Theorem [Elektronische Daten] [M.G. Beaty, M.M. Dodson, S.P. Eveson] 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 Birkhauser Boston, 2007 Beaty M.G. Department of Mathematics, University of Newcastle, Newcastle NE1 7RU, UK aut Dodson M.M. Department of Mathematics, University of York, York YO10 5DD, UK aut Eveson S.P. Department of Mathematics, University of York, York YO10 5DD, UK aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/2(2007-04-01), 187-196 1069-5869 13:2<187 2007 13 41 https://doi.org/10.1007/s00041-006-6025-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6025-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Beaty M.G. Department of Mathematics, University of Newcastle, Newcastle NE1 7RU, UK aut NATIONALLICENCE 700 1- Dodson M.M. Department of Mathematics, University of York, York YO10 5DD, UK aut NATIONALLICENCE 700 1- Eveson S.P. Department of Mathematics, University of York, York YO10 5DD, UK aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/2(2007-04-01), 187-196 1069-5869 13:2<187 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer