Best Polynomial Approximations in $L_2$ and Widths of Some Classes of Functions

  • S. B. Vakarchuk Днепропетр. ун-т им. А. Нобеля
  • A. N. Shchitov

Abstract

We obtain the exact values of extremal characteristics of a special form that connect the best polynomial approximations of functions $f(x) ∈ L_2^r(r ∈ ℤ_{+})$ and expressions containing moduli of continuity of the $k$th order $ω_k(f^{(r)}, t)$. Using these exact values, we generalize the Taikov result for inequalities that connect the best polynomial approximations and moduli of continuity of functions from $L_2$. For the classes $F (k, r, Ψ*)$ defined by $ω_k(f^{(r)}, t)$ and the majorant $Ψ(t)=t^{4k/π^2}$, we determine the exact values of different widths in the space $L_2$.
Published
25.11.2004
How to Cite
VakarchukS. B., and ShchitovA. N. “Best Polynomial Approximations in $L_2$ and Widths of Some Classes of Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 11, Nov. 2004, pp. 1458-66, https://umj.imath.kiev.ua/index.php/umj/article/view/3858.
Section
Research articles