Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces

Danilo Costarelli, and Gianluca Vinti. "Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces." Commentationes Mathematicae 53.2 (2013): null. <http://eudml.org/doc/292513>.

@article{DaniloCostarelli2013,
abstract = {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, $1 p$ < $\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 Fejér and B-spline kernels are also considered.},
author = {Danilo Costarelli, Gianluca Vinti},
journal = {Commentationes Mathematicae},
keywords = {Nonlinear sampling Kantorovich operators, Orlicz spaces, order of approximation, Lipschitz classes, irregular sampling},
language = {eng},
number = {2},
pages = {null},
title = {Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces},
url = {http://eudml.org/doc/292513},
volume = {53},
year = {2013},
}

TY - JOUR
AU - Danilo Costarelli
AU - Gianluca Vinti
TI - Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces
JO - Commentationes Mathematicae
PY - 2013
VL - 53
IS - 2
SP - null
AB - 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, $1 p$ < $\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 Fejér and B-spline kernels are also considered.
LA - eng
KW - Nonlinear sampling Kantorovich operators, Orlicz spaces, order of approximation, Lipschitz classes, irregular sampling
UR - http://eudml.org/doc/292513
ER -