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A $q$-sampling theorem related to the $q$-Hankel transform

Author: L. D. Abreu
Journal: Proc. Amer. Math. Soc. 133 (2005), 1197-1203
MSC (2000): Primary 33D15, 33D05; Secondary 94A20
Published electronically: October 14, 2004
MathSciNet review: 2117222
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Abstract: A $q$-version of the sampling theorem is derived using the $q$-Hankel transform introduced by Koornwinder and Swarttouw. The sampling points are the zeros of the third Jackson $q$-Bessel function.

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Additional Information

L. D. Abreu
Affiliation: Department of Mathematics, Universidade de Coimbra, Portugal

Keywords: Sampling theorem, reproducing kernel, $q$-Bessel functions, $q$-Hankel transform
Received by editor(s): November 21, 2003
Received by editor(s) in revised form: December 12, 2003
Published electronically: October 14, 2004
Additional Notes: Partial financial assistance by Fundação para a Ciência e Tecnologia and Centro de Matemática da Universidade de Coimbra
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2004 American Mathematical Society