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

Danilo Costarelli; Gianluca Vinti — 2011

Bollettino dell'Unione Matematica Italiana

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...

Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces

Danilo Costarelli; Gianluca Vinti — 2013

Commentationes Mathematicae

In this paper, we study the rate of approximation for the nonlinear sampling Kantorovich operators. We consider the case of uniformly continuous and bounded functions belonging to Lipschitz classes of the Zygmund-type, as well as the case of functions in Orlicz spaces. We estimate the aliasing errors with respect to the uniform norm and to the modular functional of the Orlicz spaces, respectively. The general setting of Orlicz spaces allows to deduce directly the results concerning the rate of convergence...

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