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Approximation of Classes of \({\bar \psi }\)-Integrals of Periodic Functions of Many Variables by Rectangular Linear Means of Their Fourier Series

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We obtain asymptotic equalities for deviations of rectangular linear means of Fourier series on classes of \({\bar \psi }\)-integrals of functions of many variables.

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REFERENCES

  1. A. I. Stepanets, “Rate of convergence of Fourier series on classes of \({\bar \psi }\)-integrals,” Ukr. Mat. Zh., 49, No.8, 1069–1113 (1997).

    Google Scholar 

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

    Google Scholar 

  3. A. I. Stepanets, Uniform Approximations by Trigonometric Polynomials [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  4. A. I. Stepanets, “Classification of periodic functions and the rate of convergence of their Fourier series,” Izv. Akad. Nauk SSSR, Ser. Mat., 50, No.1, 101–136 (1986).

    Google Scholar 

  5. A. I. Stepanets, Methods of Approximation Theory [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002).

    Google Scholar 

  6. V. I. Rukasov, O. A. Novikov, and S. O. Chaichenko, “Approximation of the classes \(C_\infty ^{\bar \psi }\) by de la Vallee-Poussin sums,” in: Theory of Approximation of Functions and Their Application [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002), pp. 396–406.

    Google Scholar 

  7. A. I. Stepanets and N. L. Pachulia, “Multiple Fourier sums on sets of (ψ, β)-differentiable functions,” Ukr. Mat. Zh., 43, No.4, 545–555 (1991).

    Google Scholar 

  8. N. L. Lasuriya, “Multiple Fourier sums on sets of \({\bar \psi }\)-differentiable functions,” Ukr. Mat. Zh., 55, No.7, 911–918 (2003).

    Google Scholar 

  9. P. V. Zaderei, “Integral representations of deviations of linear means of Fourier series on classes of differentiable periodic functions of two variables,” in: V. K. Dzyadyk (editor), Some Problems in the Theory of Approximation of Functions [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1985), pp. 16–28.

    Google Scholar 

  10. A. I. Stepanets, “Approximation of some classes of differentiable periodic functions of two variables by Fourier sums,” Ukr. Mat. Zh., 25, No.5, 599–609 (1973).

    Google Scholar 

  11. A. I. Stepanets, Investigation of Extremal Problems in the Theory of Summation of Fourier Series [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Kiev (1974).

  12. V. I. Rukasov, O. A. Novikov, and V. I. Bodraya, “Approximation of classes of \({\bar \psi }\)-integrals of periodic functions of two variables by linear methods,” in: O. I. Stepanets' (editor), Problems of the Theory of Approximation of Functions and Related Problems, Vol. 1, No.1, Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (2004), pp. 250–269.

    Google Scholar 

  13. S. A. Telyakovskii, “On the norms of trigonometric polynomials and approximation of differentiable functions by linear means of their Fourier series. I,” Tr. Mat. Inst. Akad. Nauk SSSR, 62, 61–97 (1961).

    Google Scholar 

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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 564–570, April, 2005.

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Rukasov, V.I., Novikov, O.A. & Bodraya, V.I. Approximation of Classes of \({\bar \psi }\)-Integrals of Periodic Functions of Many Variables by Rectangular Linear Means of Their Fourier Series. Ukr Math J 57, 678–685 (2005). https://doi.org/10.1007/s11253-005-0219-2

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  • DOI: https://doi.org/10.1007/s11253-005-0219-2

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