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

Ciaurri, Óscar; Varona, Juan

doi:10.1090/S0002-9939-07-08831-4

A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform
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by Óscar Ciaurri and Juan L. Varona PDF

Proc. Amer. Math. Soc. 135 (2007), 2939-2947 Request permission

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 $L^2((-1,1),|x|^{2\alpha +1} dx)$. This orthonormal system is a generalization of the classical exponential system defining Fourier series.

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