Advertisement

The approximation of continuous periodic functions of two variables by Faward sums

  • A. I. Stepanets
Article
  • 31 Downloads

Abstract

An estimate is given of the magnitude of the exact upper bound of the errors of double Faward sums on classes of continuous periodic functions, and asymptotic equations are found in the case of the classes H A,B α,β for these quantities, expressed in terms of the exact upper bounds of the errors of Faward sums on the classes H A α and H B β of functions of one variable.

Keywords

Periodic Function Asymptotic Equation Continuous Periodic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    J. Faward, “Sur les meilleurs procédes d'approximation de certaines classes de fonctions par des polynomes trigonométriques,” Bull. Sci. Math.,61(2), 209–224, 243–256 (1937).Google Scholar
  2. 2.
    N. I. Akhiezer, Lectures on Approximation Theory [in Russian], 2nd Edition, Moscow (1965).Google Scholar
  3. 3.
    S. B. Stechkin, “On the approximation of continuous periodic functions by Faward sums,” Tr. Matem. Inst. Akad. Nauk SSSR,109, 26–34 (1971).Google Scholar
  4. 4.
    I. K. Daugavet, “On a property of completely continuous operators in the space C,” Uspekhi Matem. Nauk,18, No. 5, 157–158 (1963).Google Scholar
  5. 5.
    N. P. Korneichuk, “On an estimate of the approximation of functions of classes by trigonometric polynomials,” Sb. Investigations on Contemporary Problems of the Constructive Theory of Functions,1, 148–154 (1961).Google Scholar
  6. 6.
    A. I. Stepanets, “On a problem of A. N. Kolmogorov in the case of functions of two variables,” Ukrain. Matem. Zh.,24, No. 5, 653–666 (1972).Google Scholar

Copyright information

© Consultants Bureau 1973

Authors and Affiliations

  • A. I. Stepanets
    • 1
  1. 1.Institute of MathematicsAcademy of Sciences of the Ukrainian SSRUkraine

Personalised recommendations