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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 Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform


Authors: Óscar Ciaurri and Juan L. Varona
Journal: Proc. Amer. Math. Soc. 135 (2007), 2939-2947
MSC (2000): Primary 94A20; Secondary 42A38
Published electronically: May 8, 2007
MathSciNet review: 2317972
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Abstract: A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform on the real line is proved. To this end we state, in terms of Bessel functions, an orthonormal system which is complete in $ L^2((-1,1),\vert x\vert^{2\alpha+1}\,dx)$. This orthonormal system is a generalization of the classical exponential system defining Fourier series.


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Additional Information

Óscar Ciaurri
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain
Email: oscar.ciaurri@dmc.unirioja.es

Juan L. Varona
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain
Email: jvarona@dmc.unirioja.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08831-4
PII: S 0002-9939(07)08831-4
Keywords: WSK sampling theorem, reproducing kernel, Dunkl transform, orthonormal system, Bessel functions
Received by editor(s): February 9, 2006
Received by editor(s) in revised form: June 6, 2006
Published electronically: May 8, 2007
Additional Notes: Research supported by grant MTM2006-13000-C03-03 of the DGI
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.