A Whittaker-shannon-kotel’nikov Sampling Theorem Related to the Dunkl Transform
نویسنده
چکیده
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 L2((−1, 1), |x|2α+1 dx). This orthonormal system is a generalization of the classical exponential system defining Fourier series.
منابع مشابه
An uncertainty inequality for Fourier-Dunkl series
An uncertainty inequality for the Fourier–Dunkl series, introduced by the authors in [Ó. Ciaurri and J. L. Varona, A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform, Proc. Amer. Math. Soc. 135 (2007), 2939–2947], is proved. This result is an extension of the classical uncertainty inequality for the Fourier series.
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