Constructive Approximation in Mixed norm Spaces

TL;DR

This paper investigates function approximation in mixed norm Lebesgue and Orlicz spaces using Kantorovich-type sampling operators, establishing their boundedness and approximation properties in these generalized spaces.

Contribution

It introduces the boundedness and approximation analysis of Kantorovich sampling operators specifically in mixed norm Lebesgue and Orlicz spaces, expanding the understanding of approximation in these complex spaces.

Findings

Boundedness of Kantorovich sampling operators in mixed norm spaces

Approximation properties of these operators in Lebesgue and Orlicz spaces

Examples of kernels suitable for the approximation process

Abstract

The concept of mixed norm spaces has emerged as a significant interest in fields such as harmonic analysis. In addition, the problem of function approximation through sampling series has been particularly noteworthy in the realm of approximation theory. This paper aims to address both these aspects. Here we deal with the problem of function approximation in diverse mixed norm function spaces. We utilise the family of Kantorovich type sampling operators as approximator for the functions in mixed norm Lebesgue space, and mixed norm Orlicz space. The Orlicz spaces are well-known as a generalized family that encompasses many significant function spaces. We establish the boundedness of the family of generalized as well as Kantorovich type sampling operators within the framework of these mixed norm spaces.Further, we study the approximation properties of Kantorovich-type sampling operators in both mixed norm Lebesgue and Orlicz spaces. At the end, we discuss a few examples of suitable kernel involved in the discussed approximation procedure.