In this paper, we study the problem of the rate of approximation for the family of sampling Kantorovich operators in the uniform norm, for uniformly continuous and bounded functions belonging to Lipschitz classes (Zygmund-type classes), and for functions in Orlicz spaces. The general setting of Orlicz spaces allows us to directly deduce the results concerning the order of approximation in LP-spaces, 1 <= p < infinity, very useful in applications to Signal Processing, in Zygmund spaces and in exponential spaces. Particular cases of the sampling Kantorovich series based on Fejer's kernel and B-spline kernels are studied in detail.
Order of approximation for Sampling Kantorovich Operators
COSTARELLI, Danilo;VINTI, Gianluca
2014
Abstract
In this paper, we study the problem of the rate of approximation for the family of sampling Kantorovich operators in the uniform norm, for uniformly continuous and bounded functions belonging to Lipschitz classes (Zygmund-type classes), and for functions in Orlicz spaces. The general setting of Orlicz spaces allows us to directly deduce the results concerning the order of approximation in LP-spaces, 1 <= p < infinity, very useful in applications to Signal Processing, in Zygmund spaces and in exponential spaces. Particular cases of the sampling Kantorovich series based on Fejer's kernel and B-spline kernels are studied in detail.File in questo prodotto:
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