Asymptotic estimates for the widths of classes of functions of high smothness - Serdyuk, A.S.; Sokolenko, I.V. (Carpathian Mathematical Publications, 2023)
We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of 2π-periodic functions φ, such that \|φ\|_21, with fixed generated kernels Ψ_β , which have Fourier series of the form _k=1^∞ ψ(k)(kt-β_kπ/2), where ψ(k)0, ψ^2(k)<∞, β_kR. It is shown that for rapidly decreasing sequences ψ(k) (in particular, if _k→∞ψ(k+1)/ψ(k)=0) the obtained estimates are asymptotic equalities. We establish that asymptotic equalities for widths of this classes are realized by trigonometric Fourier sums.