Approximation of $\bar {ω}$ -integrals of continuous functions defined on the real axis by Fourier operators - Sokolenko, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We obtain asymptotic formulas for the deviations of Fourier operators on the classes of continuous functions $C^{ψ}_{∞}$ and $\hat{C}^{\bar{ψ} } H_{ω}$ in the uniform metric. We also establish asymptotic laws of decrease of functionals characterizing the problem of the simultaneous approximation of $\bar{ψ}$-integrals of continuous functions by Fourier operators in the uniform metric.