Multidimensional sampling-Kantorovich operators in BV-spaces

Abstract

The main purpose of this article is to prove a result of convergence in variation for a family of multidimensional sampling-Kantorovich operators in the case of averaged-type kernels. The setting in which we work is that one of BV-spaces in the sense of Tonelli.

Kantorovich Version of Vector-Valued Shepard Operators

“…There are numerous studies in the literature related to Kantorovich operators. Especially in recent years, it has also been shown that these operators have significant advantages in fields such as artificial neural networks, signal and digital image processing, and sampling theory (see, for instance, [4][5][6][7]).…”