Approximation of functions by linear summation methods in the Orlicz type spaces

TL;DR

This paper investigates how linear summation methods approximate functions in Orlicz type spaces, providing constructive measures of approximation quality for functions with specific smoothness properties.

Contribution

It introduces new approximation estimates for Fourier series in Orlicz spaces, linking smoothness moduli to approximation effectiveness.

Findings

Derived bounds for approximation errors in Orlicz spaces

Established constructive characteristics for function classes with bounded smoothness

Extended classical Fourier approximation results to Orlicz type spaces

Abstract

Approximative properties of linear summation methods of Fourier series are considered in the Orlicz type spaces ${\mathcal S}_{M}$. In particular, in terms of approximations by such methods, constructive characteristics are obtained for classes of functions whose smoothness moduli do not exceed a certain majorant.