Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces

TL;DR

This paper investigates the approximation rates of multivariate sampling Kantorovich operators across various function spaces, including Lipschitz, Orlicz, and Lp spaces, providing theoretical insights and specific kernel-based cases.

Contribution

It introduces new approximation order results for these operators in different function spaces and explores their applications with specific kernels like Fejer and B-spline.

Findings

Established approximation rates in Lipschitz and Orlicz spaces.

Analyzed multivariate sampling Kantorovich operators with product-type kernels.

Extended results to Lp, interpolation, and exponential spaces.

Abstract

In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of the uniform approximation for uniformly continuous and bounded functions/signals belonging to Lipschitz classes and the case of the modular approximation for functions in Orlicz spaces are considered. In the latter context, Lipschitz classes of Zygmund-type which take into account of the modular functional involved are introduced. Applications to Lp(R^n), interpolation and exponential spaces can be deduced from the general theory formulated in the setting of Orlicz spaces. The special cases of multivariate sampling Kantorovich operators based on kernels of the product type and constructed by means of Fejer's and B-spline kernels have been studied in details.