Costarelli, Danilo and Vinti, Gianluca:
Approximation by Multivariate Generalized Sampling Kantorovich Operators in the Setting of Orlicz Spaces
Bollettino dell'Unione Matematica Italiana Serie 9 4 (2011), fasc. n.3, p. 445-468, (English)
pdf (743 Kb), djvu (339 Kb). | MR 2906770 | Zbl 1234.41018
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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.
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