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Approximation of classes of analytic functions by a linear method of special form

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We establish asymptotic equalities for the least upper bounds of deviations of trigonometric polynomials generated by a linear approximation method of a special form on classes of convolutions of analytic functions in the uniform and integral metrics.

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References

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    A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 1, Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, Ukraine (2002); English translation: VSP, Leiden (2005).

  2. 2.

    A. I. Stepanets’ and A. S. Serdyuk, “Approximation by Fourier sums and best approximations on classes of analytic functions,” Ukr. Mat. Zh., 52, No. 3, 375–395 (2000); English translation: Ukr. Math. J., 52, No. 3, 433–456 (2000).

  3. 3.

    A. S. Serdyuk, “On one linear method for approximation of periodic functions,” in: Problems in Approximation Theory and Related Topics [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2004), pp. 295–336.

  4. 4.

    A. S. Serdyuk, “Approximation of Poisson integrals by one linear approximation method in uniform and integral metrics,” Ukr. Mat. Zh., 60, No. 7, 976–982 (2008); English translation: Ukr. Math. J., 60, No. 7, 1144–1152 (2008).

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    M. F. Timan, Approximation and Properties of Periodic Functions [in Russian], Naukova Dumka, Kiev (2009).

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Author information

Correspondence to A. S. Serdyuk.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 1, pp. 102–109, January, 2011.

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Serdyuk, A.S., Chaichenko, S.O. Approximation of classes of analytic functions by a linear method of special form. Ukr Math J 63, 125 (2011). https://doi.org/10.1007/s11253-011-0491-2

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Keywords

  • Analytic Function
  • Fourier Series
  • Special Form
  • Periodic Function
  • Integrable Function