Asymptotic estimates for the widths of classes of functions of high smothness

Authors

  • A.S. Serdyuk Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01601, Kyiv, Ukraine
  • I.V. Sokolenko Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01601, Kyiv, Ukraine https://orcid.org/0000-0002-8534-4616
https://doi.org/10.15330/cmp.15.1.246-259

Keywords:

Bernstein width, Kolmogorov width, linear width, projection width, Fourier sum, Weyl-Nagy class, class of the generalized Poisson integrals, (ψ,ˉβ)-integral, asymptotic equality
Published online: 2023-06-30

Abstract

We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of 2π-periodic functions φ, such that φ21, with fixed generated kernels Ψˉβ, which have Fourier series of the form k=1ψ(k)cos(ktβkπ/2), where ψ(k)0, ψ2(k)<,βkR. It is shown that for rapidly decreasing sequences ψ(k) (in particular, if lim) the obtained estimates are asymptotic equalities. We establish that asymptotic equalities for widths of this classes are realized by trigonometric Fourier sums.

How to Cite
(1)
Serdyuk, A.; Sokolenko, I. Asymptotic Estimates for the Widths of Classes of Functions of High Smothness. Carpathian Math. Publ. 2023, 15, 246-259.