Estimates for approximation characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of many variables with a given majorant of the mixed moduli of continuity

TL;DR

This paper derives order estimates for approximating classes of multivariable periodic functions with specified smoothness constraints using orthogonal projection and linear operators.

Contribution

It provides new order estimates for approximation of classes $B^{ omannumeral1}_{p, heta}$ in $L_q$ spaces, expanding understanding of multivariable function approximation.

Findings

Order estimates of approximation are established.

Results apply to classes with given majorants of mixed moduli of continuity.

The work advances approximation theory for multivariable periodic functions.

Abstract

We obtain order estimates of approximation of classes $B^{\Omega}_{p,\theta}$ of periodic functions of many variables in the space $L_q$ by using operators of orthogonal projection as well as linear operators subjected to some conditions.