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A  -sampling theorem related to the  -Hankel transform
Author(s):
L.
D.
Abreu
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1197-1203.
MSC (2000):
Primary 33D15, 33D05;
Secondary 94A20
Posted:
October 14, 2004
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Additional information
Abstract:
A  -version of the sampling theorem is derived using the  -Hankel transform introduced by Koornwinder and Swarttouw. The sampling points are the zeros of the third Jackson  -Bessel function.
References:
-
- 1.
- L. D. Abreu, J. Bustoz, Complete sets of q-Bessel functions, to appear in ``Theory and Applications of Special Functions. A volume dedicated to Mizan Rahman'', (eds. M. E. H. Ismail and E. Koelink), Developments in Mathematics, Kluwer Acad. Publ.
- 2.
- L. D. Abreu, J. Bustoz, J. L. Cardoso, The roots of the third Jackson q-Bessel function, Internat. J. Math. Math. Sci. 67, (2003), 4241-4248.
- 3.
- G. Gasper and M. Rahman, ``Basic Hypergeometric Series,'' Cambridge University Press, Cambridge, UK, 1990. MR 91d:33034
- 4.
- G. H. Hardy, Notes on special systems of orthogonal functions IV, Proc. Cambridge Phil. Soc., 37 (1941), 331-348. MR 3:108b
- 5.
- J. R. Higgins, An interpolation series associated with the Bessel-Hankel transform, J. Lond. Math. Soc. 5, (1972) 707-714. MR 47:9152
- 6.
- M. E. H. Ismail, The Zeros of Basic Bessel functions, the functions
 , and associated orthogonal polynomials, J. Math. Anal. Appl. 86 (1982), 1-19. MR 83c:33010 - 7.
- H. T. Koelink, R. F. Swarttouw, On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials, J. Math. Anal. Appl. 186, (1994), 690-710. MR 95j:33050
- 8.
- T. H. Koornwinder, R. F. Swarttouw, On q-analogues of the Fourier and Hankel transforms. Trans. Amer. Math. Soc. 333 (1992), no. 1, 445-461. MR 92k:33013
- 9.
- A. A. Kvitsinsky, Spectral zeta functions for q-Bessel equations, J. Phys. A: Math. Gen. 28, 1753-1764 (1995), no. 6. MR 96f:58181
- 10.
- L. Máté, ``Hilbert space methods in science and engineering''. Adam Hilger, Ltd., Bristol, 1989.MR 92e:46002
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Additional Information:
L.
D.
Abreu
Affiliation:
Department of Mathematics, Universidade de Coimbra, Portugal
Email:
daniel@mat.uc.pt.
DOI:
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
Posted:
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
Copyright of article:
Copyright
2004,
American Mathematical Society
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