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Exact order of approximation of periodic functions by one nonclassical method of summation of Fourier series

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Ukrainian Mathematical Journal Aims and scope

By using an exact estimate for approximation by known trigonometric polynomials, we strengthen a Jackson-type theorem. Moreover, we determine the exact order of approximation of some periodic functions by these polynomials. For this purpose, we introduce a special modulus of smoothness.

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References

  1. A. F. Timan, Theory of Approximation of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow (1960).

    Google Scholar 

  2. R. M. Trigub and E. S. Belinsky, Fourier Analysis and Approximation of Functions, Kluwer, Dordrecht (2004).

    Book  MATH  Google Scholar 

  3. R. M. Trigub, “Exact order of approximation of periodic functions by linear positive operators,” East J. Approxim., 15, No. 1, 25–50 (2009).

    MathSciNet  MATH  Google Scholar 

  4. B. R. Draganov, “Exact estimates of the rate of approximation of convolution operators,” J. Approxim. Theory, 162, 952–979 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  5. S. B. Stechkin, “On the order of the best approximations of continuous functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 15, No. 3, 219–242 (1951).

    MATH  Google Scholar 

  6. E. M. Stein and G. Weiss, Introduction to Fourier Analysis of Euclidean Spaces, Princeton University, Princeton (1971).

    Google Scholar 

  7. R. E. Edwards, Fourier Series. A Modern Introduction, Vol. 2, Springer, New York (1982).

    Book  MATH  Google Scholar 

  8. E. Liflyand, S. Samko, and R. Trigub, “TheWiener algebra of absolutely convergent Fourier integrals: an overview,” Anal. Math. Phys., 2, 1–68 (2012); E. Liflyand, S. Samko, and R. Trigub, Known and New Results on Absolute Convergence of Fourier Integrals, Preprint No. 859, Centre de Recerca Matemàtica (2009).

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Authors and Affiliations

  1. Donetsk National University, Donetsk, Ukraine

    O. V. Kotova

Authors
  1. O. V. Kotova
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  2. R. M. Trigub
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 7, pp. 954–969, July, 2012.

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Kotova, O.V., Trigub, R.M. Exact order of approximation of periodic functions by one nonclassical method of summation of Fourier series. Ukr Math J 64, 1090–1108 (2012). https://doi.org/10.1007/s11253-012-0701-6

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  • DOI: https://doi.org/10.1007/s11253-012-0701-6

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