Journal of Integral Equations and Applications

Order of approximation for sampling Kantorovich operators

Danilo Costarelli and Gianluca Vinti

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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 $L^p$-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.

Article information

Source
J. Integral Equations Applications, Volume 26, Number 3 (2014), 345-367.

Dates
First available in Project Euclid: 31 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1414761102

Digital Object Identifier
doi:10.1216/JIE-2014-26-3-345

Mathematical Reviews number (MathSciNet)
MR3273899

Zentralblatt MATH identifier
1308.41016

Subjects
Primary: 41A25: Rate of convergence, degree of approximation 41A30: Approximation by other special function classes 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47A58: Operator approximation theory 47B38: Operators on function spaces (general) 94A12: Signal theory (characterization, reconstruction, filtering, etc.)

Keywords
Sampling Kantorovich operators Orlicz spaces order of approximation Lipschitz classes irregular sampling

Citation

Costarelli, Danilo; Vinti, Gianluca. Order of approximation for sampling Kantorovich operators. J. Integral Equations Applications 26 (2014), no. 3, 345--367. doi:10.1216/JIE-2014-26-3-345. https://projecteuclid.org/euclid.jiea/1414761102


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