Widths of some classes of functions defined by the generalized moduli of continuity ωγ in the space L2

Abstract

The exact values of some widths for the classes of functions \( {H}^{\omega_{\gamma }} \) and \( {W}_{\beta, 2}^{\psi}\left({\omega}_{\gamma },\varPhi \right) \) given by the generalized modulus of continuity ω_γ and the majorant Φ satisfying a certain condition are computed. On the indicated classes, the exact values of Fourier coefficients are found.