## Journal of Integral Equations and Applications

### Order of approximation for sampling Kantorovich operators

#### 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

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

#### 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