Exact values of widths of certain classes of periodic differentiable functions in the space L2[0, 2π]Точные значение поперечников некоторых классов периодических дифференцируемых функциИ в пространстве L2 [0, 2п]

In the paper we find the exact values of different n-widths of such periodic functions in these space L2[0, 2π] that satisfy the restriction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\frac{2} {{h^2 }}\int_0^h {t\omega _m^p \left( {f^{(r)} ;t} \right)dt} } \right)^{2/p} \leqslant \Phi (h),$$\end{document} where 0 < h < ∞, 2/r < p ≤ 2, r ≥ 2, r ∈ N, while ωm(f(r); t) is the modulus of continuity of mth order of the derivative f(r) ∈ L2[0, 2π], and Φ(u) is an arbitrary continuous, increasing function and Φ(0) = 0.