A Paley-Wiener theorem for the Askey-Wilson function transform

• Author(s): Abreu, Luis Daniel ; Bouzeffour, Fethi
• Date: 2009
• Persistent ID: http://hdl.handle.net/10316/11165
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Askey-Wilson function; Paley-Wiener theorem; Reproducing Kernels; Sampling Theorem
• Document Type: Preprint
• Language: English

Description

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. CMUC/FCT; FCT post-doctoral grant SFRH/BPD/26078/2005, POCI 2010; FSE