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 $C^{ψ}_{∞}$ 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.