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https://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: | https://hdl.handle.net/10316/11165 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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File | Description | Size | Format | |
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A Paley-Wiener theorem for the Askey-Wilson.pdf | 134.04 kB | Adobe PDF | View/Open |
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