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Approximation of classes\(C_\infty ^{\bar \psi } \) by zygmund sumsby zygmund sums

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Abstract

We consider the approximation of functions of the classes of\(\bar \psi \) by Zygmund sums. In papticular, we present asymptotic equalities for the quantities\(\varepsilon _n (C_\infty ^{\bar \psi } ;Z_n )_C \) under various conditions imposed on functions ψ1(·) and ψ2(·).

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References

  1. A. Zygmund, “The approximation of functions by typical means of their Fourier series,”Duke Math. J.,12, 695–704 (1945).

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  2. A. I. Stepanets, “Convergence rate of Fourier series on the classes of\(\bar \psi \)-integrals,”Ukr. Mat. Zh.,49, No. 8, 1069–1113 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  3. D. N. Bushev,Approximation of Classes of Continuous Periodic Functions by Zygmund Sums [in Russian], Preprint No. 56, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1984).

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

    MATH  Google Scholar 

  5. A. I. Stepanets, “Approximation of\(\bar \psi \)-integrals of periodic functions by Fourier sums (small smoothness). II,”Ukr. Mat. Zh.,50, No. 3, 388–400 (1997).

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  6. V. I. Rukasov and S. O. Chaichenko, “Approximation of\(\bar \psi \)-integrals of 2π-periodic functions by de la Vallée-Poussin sums,” in:Fourier Series. Theory and Applications [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998), pp. 242–254.

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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. 856–860, June, 2000.

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Fedorenko, A.S. Approximation of classes\(C_\infty ^{\bar \psi } \) by zygmund sumsby zygmund sums. Ukr Math J 52, 981–986 (2000). https://doi.org/10.1007/BF02591794

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  • DOI: https://doi.org/10.1007/BF02591794

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