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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Email: daniel@mat.uc.pt.

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07589-6
PII: S 0002-9939(04)07589-6
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