Open Access
FALL 2014 Order of approximation for sampling Kantorovich operators
Danilo Costarelli, Gianluca Vinti
J. Integral Equations Applications 26(3): 345-367 (FALL 2014). DOI: 10.1216/JIE-2014-26-3-345


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 $L^p$-spaces, $1 \le p \lt \infty$, very useful in applications to Signal Processing, in Zygmund spaces and in exponential spaces. Particular cases of the sampling Kantorovich series based on Fej\'er's kernel and B-spline kernels are studied in detail.


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Danilo Costarelli. Gianluca Vinti. "Order of approximation for sampling Kantorovich operators." J. Integral Equations Applications 26 (3) 345 - 367, FALL 2014.


Published: FALL 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1308.41016
MathSciNet: MR3273899
Digital Object Identifier: 10.1216/JIE-2014-26-3-345

Primary: 41A25 , 41A30 , 46E30 , 47A58 , 47B38 , 94A12

Keywords: Irregular sampling , Lipschitz classes , order of approximation , Orlicz spaces , Sampling Kantorovich operators

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.26 • No. 3 • FALL 2014
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