Year: 2018
Type: article
Abstract: 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 Fejér and the Bochner-Riesz kernels (bandlimited functions).
Institution: University of Perugia
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2764239685