Approximation by linear methods of classes of $(\psi,\bar\beta)-$differentiable functions

TL;DR

This paper determines the maximum approximation errors achievable by linear Fourier series summation methods for specific classes of periodic functions characterized by multiplier sequences and argument shifts.

Contribution

It provides explicit bounds for approximation errors in the $L_2$ metric for classes of functions defined by $(areta,areta)$-differentiability and multiplier sequences.

Findings

Calculated upper bounds for approximation errors in $L_2$ norm.

Analyzed classes of functions with specific multiplier and shift sequences.

Enhanced understanding of approximation limits for Fourier series methods.

Abstract

We calculate the least upper bounds for approximations in the metric of the space $L_2$ by linear methods of summation of Fourier series on classes of periodic functions $L^\psi_{\bar\beta,1}$ defined by sequences of multipliers $\psi=\psi(k)$ and shifts of argument $\bar\beta=\beta_k$.