Ukrainian Mathematical Journal

, Volume 64, Issue 7, pp 1090–1108 | Cite as

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

  • O. V. Kotova
  • R. M. Trigub

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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  1. 1.
    A. F. Timan, Theory of Approximation of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow (1960).Google Scholar
  2. 2.
    R. M. Trigub and E. S. Belinsky, Fourier Analysis and Approximation of Functions, Kluwer, Dordrecht (2004).MATHCrossRefGoogle Scholar
  3. 3.
    R. M. Trigub, “Exact order of approximation of periodic functions by linear positive operators,” East J. Approxim., 15, No. 1, 25–50 (2009).MathSciNetMATHGoogle Scholar
  4. 4.
    B. R. Draganov, “Exact estimates of the rate of approximation of convolution operators,” J. Approxim. Theory, 162, 952–979 (2010).MathSciNetMATHCrossRefGoogle Scholar
  5. 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).MATHGoogle Scholar
  6. 6.
    E. M. Stein and G. Weiss, Introduction to Fourier Analysis of Euclidean Spaces, Princeton University, Princeton (1971).Google Scholar
  7. 7.
    R. E. Edwards, Fourier Series. A Modern Introduction, Vol. 2, Springer, New York (1982).MATHCrossRefGoogle Scholar
  8. 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).Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • O. V. Kotova
    • 1
  • R. M. Trigub
  1. 1.DonetskUkraine

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