On trigonometric approximation of functions in the Lp norm

TL;DR

This paper investigates how well functions can be approximated in the Lp norm using Fourier series-based operators, extending previous results with weaker assumptions on the matrices involved.

Contribution

It introduces generalized approximation results in Lp spaces using Fourier series operators with less restrictive conditions on the matrices.

Findings

Derived new bounds for approximation degree in Lp norm

Extended classical results to broader classes of operators

Reduced assumptions on the matrices used in approximation

Abstract

In this paper we obtain degree of approximation of functions in Lp by operators associated with their Fourier series using integral modulus of continuity. These results generalize many know results and are proved under less stringent conditions on the infinite matrix.