Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/11165
Title: A Paley-Wiener theorem for the Askey-Wilson function transform
Authors: Abreu, Luís Daniel 
Bouzeffour, Fethi 
Keywords: Askey-Wilson function; Paley-Wiener theorem; Reproducing Kernels; Sampling Theorem
Issue Date: 2009
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 09-22 (2009)
Abstract: We define an analogue of the Paley-Wiener space in the context of the Askey-Wilson function transform, compute explicitly its reproducing kernel and prove that the growth of functions in this space of entire functions is of order two and type ln q−1, providing a Paley-Wiener Theorem for the Askey-Wilson transform. Up to a change of scale, this growth is related to the refined concepts of exponential order and growth proposed by J. P. Ramis. The Paley-Wiener theorem is proved by combining a sampling theorem with a result on interpolation of entire functions due to M. E. H. Ismail and D. Stanton.
URI: http://hdl.handle.net/10316/11165
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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