Approximation of $$\bar \omega $$ -integrals of continuous functions defined on the real axis by Fourier operators

Abstract

We obtain asymptotic formulas for the deviations of Fourier operators on the classes of continuous functions \(\hat C_\infty ^{\bar \psi } \) and \(\hat C^{\bar \psi } H_\omega \) in the uniform metric. We also establish asymptotic laws of decrease of functionals characterizing the problem of the simultaneous approximation of \({\bar \psi }\)-integrals of continuous functions by Fourier operators in the uniform metric.