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

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