A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform

A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform on the real line is proved. To this end we state, in terms of Bessel functions, an orthonormal system which is complete in L<sup>2</sup>((-1, 1), |x|<sup>2α+1</sup> dx). This orthonormal syst...

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Detalhes bibliográficos
Autores: Ciaurri, O. [0000-0002-1695-3311], Varona, J.L. [0000-0002-2023-9946]
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2007
País:España
Recursos:Universidad de La Rioja (UR)
Repositório:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc69cab750603269e8217c
Acesso em linha:https://investigacion.unirioja.es/documentos/5bbc69cab750603269e8217c
Access Level:Acceso aberto
Palavra-chave:Bessel functions
Dunkl transform
Orthonormal system
Reproducing kernel
WSK sampling theorem
Descrição
Resumo:A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform on the real line is proved. To this end we state, in terms of Bessel functions, an orthonormal system which is complete in L<sup>2</sup>((-1, 1), |x|<sup>2α+1</sup> dx). This orthonormal system is a generalization of the classical exponential system defining Fourier series. © 2007 American Mathematical Society.