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Bestm-term trigonometric approximations of classes of (Ψ, β)-differentiable functions of one variable

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Abstract

We obtain an estimate exact in order for the best trigonometric approximation of classes\(L_{\beta ,p}^\psi \) of functions of one variable in the spaceL q in the case where 1<p≤2≤q<∞.

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References

  1. S. B. Stechkin, “On the absolute convergence of orthogonal series,”Dokl. Akad. Nauk SSSR,102, No. 1, 37–40 (1995).

    Google Scholar 

  2. R. S. Ismagilov, “Widths of sets in linear normed spaces and approximation of functions by trigonometric polynomials,”Usp. Mat. Nauk,29, Issue 3, 161–178 (1974).

    MathSciNet  Google Scholar 

  3. V. N. Temlyakov,Approximation of Functions with Bounded Mixed Derivatives [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  4. É. S. Belinskii, “Approximation by a “floating” system of exponents on classes of smooth periodic functions,”Mat. Sb.,132, No. 1, 20–27 (1987).

    Google Scholar 

  5. A. S. Romanyuk, “The best trigonometric and bilinear approximations of functions of many variables from the classes\(B_{p,\theta }^r \),”Ukr. Mat. Zh.,44, No. 11, 1535–1547 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  6. A. I. Stepanets,Classes of Periodic Functions and Approximation of Their Elements by Fourier Sums [in Russian], Preprint No. 10, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1983).

    Google Scholar 

  7. A. I. Stepanets,Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).

    MATH  Google Scholar 

  8. A. Zygmund,Trigonometric Series, Vol. 2, Cambridge University, Cambridge (1959).

    MATH  Google Scholar 

  9. A. S. Romanyuk, “Inequalities forL q -norms of (Ψ,β)-derivatives andn-widths of classes of functions of many variables,” in:Investigations on the Theory of Approximation of Functions [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987), pp. 92–105.

    Google Scholar 

  10. S. M. Nikol'skii,Approximation of Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  11. N. P. Korneichuk,Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  12. A. S. Fedorenko, “The bestm-term trigonometric approximations of functions of the classes\(L_{\beta ,p}^\psi \),” in:Fourier Series. Theory and Application [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998), pp. 356–364.

    Google Scholar 

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Authors
  1. A. S. Fedorenko
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 850–855, June, 2000.

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Fedorenko, A.S. Bestm-term trigonometric approximations of classes of (Ψ, β)-differentiable functions of one variable. Ukr Math J 52, 974–980 (2000). https://doi.org/10.1007/BF02591793

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  • DOI: https://doi.org/10.1007/BF02591793

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