Ukrainian Mathematical Journal

, Volume 49, Issue 6, pp 825–843 | Cite as

Approximation of classes of convolutions by linear methods of summation of Fourier series

  • D. M. Bushev
Article

Abstract

We consider a family of special linear methods of summation of Fourier series and establish exact equalities for the approximation of classes of convolutions with even and odd kernels by polynomials generated by these methods.

Keywords

Linear Operator Fourier Series Periodic Function Linear Method Ukrainian Academy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. I. Stepanets, Classes of Periodic Functions and Approximation of Their Elements by Fourier Sums [in Russian], Preprint No. 83.10, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1983).Google Scholar
  2. 2.
    A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).MATHGoogle Scholar
  3. 3.
    N. P. Komeichuk, Exact Constants in the Theory of Approximation [in Russian], Nauka, Moscow (1976).Google Scholar
  4. 4.
    N. P. Korneichuk, Extremal Problems in the Theory of Approximation [in Russian], Nauka, Moscow (1976).Google Scholar
  5. 5.
    N. K. Bari, Trigonometric Series [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  6. 6.
    D. N. Bushev and A. I. Stepantes, “On the approximation of weakly differentiable periodic function,” Ukr. Mat. Zh., 42, No. 3, 406–412 (1990).CrossRefGoogle Scholar
  7. 7.
    D. N. Bushev and I. R. Koval’chuk, “On the approximation of classes of convolutions,” Ukr. Mat. Zh., 45, No. 1, 26–31 (1993).MATHMathSciNetGoogle Scholar
  8. 8.
    P. P. Korovkin, “On one asymptotic property of summation of Fourier series and the best approximation of functions of the class ℤ2 by linear positive operators,” Usp. Mat. Nauk, 13, No. 6184, 99–103 (1953).MathSciNetGoogle Scholar
  9. 9.
    D. N. Bushev, “On the best asymptotic approximation of the classes of differentiable functions by linear positive operators,” Ukr. Mat. Zh., 37, No. 2, 154–162 (1985).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • D. M. Bushev

There are no affiliations available

Personalised recommendations