Geodesic
Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces
Commentationes Mathematicae, Tome 53 (2013) no. 2, p. 271−292.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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 in \(L^p\)-spaces, \(1 \miu p\) \(\infty\), very useful in the applications to Signal Processing. Others examples of Orlicz spaces as interpolation spaces and exponential spaces are discussed and the particular cases of the nonlinear sampling Kantorovich series constructed using Fej\'er and B-spline kernels are also considered.
DOI : 10.14708/cm.v53i2.792
Mots-clés : Nonlinear sampling Kantorovich operators, Orlicz spaces, order of approximation, Lipschitz classes, irregular sampling 
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Danilo Costarelli; Gianluca Vinti. Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces. Commentationes Mathematicae, Tome 53 (2013) no. 2, p.  271−292. doi : 10.14708/cm.v53i2.792. http://geodesic.mathdoc.fr/articles/10.14708/cm.v53i2.792/

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