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Ukrainian Mathematical Journal

, Volume 51, Issue 12, pp 1945–1949 | Cite as

On the bestm-term trigonometric and orthogonal trigonometric approximations of functions from the classesL Ψ β,ρ

  • A. S. Fedorenko
Brief Communications

Abstract

We obtain estimates exact in order for the best trigonometric and orthogonal trigonometric approximations of the classesL Ψ β,ρ of functions of one variable in the spaceL q in the case 2<p <q < ∞.

Keywords

Fourier Series Naukova Dumka Fourier Coefficient Approximation Theory Trigonometric Polynomial 
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.

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References

  1. 1.
    A. S. Romanyuk, “Inequalities of the Bohr-Favard type and the best M-component approximations of the classesL β,ρΨ” in:On Some Problems in the Theory of Approximation of Functions and Their Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988), pp. 98–108.Google Scholar
  2. 2.
    A. S. Fedorenko, “Best m-component trigonometric approximations of functions from the classesL Ψβ,ρ” in:Fourier Series: Theory and Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998), pp. 356–364.Google Scholar
  3. 3.
    B. S. Kashin and A. A. Saakyan,Trigonometric Series [in Russian], Nauka, Moscow (1984).Google Scholar
  4. 4.
    N. P. Korneichuk,Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).Google Scholar
  5. 5.
    A. S. Romanyuk, “Inequalities for the Lp-norms of (ψ β)-derivatives and the Kolmogorov widths of the classesL Ψβ,ρ of functions of many variables,” in:Investigations in the Theory of Approximation of Functions [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987), pp. 92–105.Google Scholar
  6. 6.
    A. I. Stepanets,Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).zbMATHGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • A. S. Fedorenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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