Bohr--Favard Inequality for differences and constants in Jackson--Stechkin Theorem

Abstract

We consider uniform approximations by trigonometric polynomials. The aim of the paper is to obtain good estimates of the Jackson--Stechkin constants $J_m$. We prove that $J_m\le C{2}^{-m+5/2{\log }_{2}m}$. Our proof is based on the difference analogue of the Bohr--Favard inequality.

6 pages