A characterization of the convergence in variation for the generalized sampling series

By L. Angeloni, Danilo Costarelli, Gianluca Vinti. Annales Academiae Scientiarum Fennicae: Mathematica, 2017

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In this paper, we study the convergence in variation for the generalized sampling operators based upon averaged-type kernels and we obtain a characterization of absolutely continuous functions. This result is proved exploiting a relation between the first derivative of the above operator acting on $f$ and the sampling Kantorovich series of f'. By such approach, also a variation detracting-type property is established. Finally, examples of averaged kernels are provided, such as the central B-splines of order $n$ (duration limited functions) or other families of kernels generated by the Fejer and the Bochner-Riesz kernels (bandlimited functions).

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

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