Approximation by Multivariate Generalized Sampling Kantorovich Operators in the Setting of Orlicz Spaces

Costarelli, Danilo ; Vinti, Gianluca

Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 3, pp. 445-468

Résumé

In this paper we study a linear version of the sampling Kantorovich type operators in a multivariate setting and we show applications to Image Processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces $L^\varphi(\mathbb{R}^n)$ that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in $L^p(\mathbb{R}^n)$- spaces, $L^\alpha\log^\beta L(\mathbb{R}^n)$-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and Image Processing applications are included.