A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform
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Universidad de La Rioja
info
ISSN: 0002-9939
Year of publication: 2007
Volume: 135
Issue: 9
Pages: 2939-2947
Type: Article
More publications in: Proceedings of the American Mathematical Society
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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<sup>2</sup>((-1, 1), |x|<sup>2α+1</sup> dx). This orthonormal system is a generalization of the classical exponential system defining Fourier series. © 2007 American Mathematical Society.