Approximation of the $\bar {\Psi}$ -integrals of functions defined on the real axis by Fourier operators

Abstract

We find asymptotic formulas for the least upper bounds of the deviations of Fourier operators on classes of functions locally summable on the entire real axis and defined by $\bar {\Psi}$-integrals. On these classes, we also obtain asymptotic equalities for the upper bounds of functionals that characterize the simultaneous approximation of several functions.