Estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations of the classes of (\psi, \beta)-differentiable functions

TL;DR

This paper derives precise estimates for Fourier-based approximations of classes of periodic functions with (,)-derivatives in L_ spaces, advancing understanding of approximation accuracy.

Contribution

It provides exact-order estimates for various Fourier approximation methods for (,)-differentiable functions in L_s spaces, a novel contribution to approximation theory.

Findings

Exact-order estimates for Fourier sums and best approximations.

Results applicable to functions with (,)-derivatives in L_.

Advances in understanding approximation accuracy for these function classes.

Abstract

We obtain the exact-order estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations in metrics of spaces L_s, 1\leq s<\infty, of classes of 2\pi-periodic functions, whose (\psi,\beta)-derivatives belong to unit ball of the space L_\infty.