Approximation of functions from Lp(w)b by matrix means of their Fourier series

TL;DR

This paper investigates how well functions from certain classes can be approximated by matrix means of their Fourier series, providing new results on approximation rates and norm estimates under specific conditions.

Contribution

It introduces new conditions and classes for matrix means of Fourier series, extending approximation results to functions in generalized Lipschitz and other classes.

Findings

Established approximation rates for functions using matrix means.

Derived norm approximation results for generalized Lipschitz classes.

Identified conditions under which Fourier series approximations are optimal.

Abstract

We formulate some special conditions for the integrable functions and moduli of continuity. We give the results on rate of approximation of such functions by matrix means of their Fourier series, where the entries of the rows of the matrix generate the sequences belonging to the classes MRBVS and MHBVS. We also present some results on norm approximation for functions from the generalized integral Lipschitz classes.