Abstract

We will present some approximation results by means of sampling-type operators in the frame of the spaces of functions with bounded variation. We will in particular focus on the multidimensional case, where we obtain estimates and convergence in variation using the concept of variation in the sense of Tonelli. Sampling-type operators are well-known and studied in Approximation Theory and their deep relations with Signal and Image Processing, together with the geometrical aspects related to the construction of the Tonelli variation, allow us to address also some applicative connections of the approximation results to problems of Digital Image Processing. The author has been partially supported within the project PRIN 2022 PNRR : “RETINA: REmote sensing daTa INversion with multivariate functional modeling for essential climAte variables characterization”, funded by the European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, under the Italian Ministry of University and Research (Project Code: P20229SH29 , CUP: J53D23015950001 ).