Skip to main content
Log in

Exact upper bound for approximations on classes of differential periodic functions using Rogosinski polynomials

  • Published:
Ukrainian Mathematical Journal Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. A. N. Kolmogorov, “Zur Grössenordnung des Restgliedes Fourierscher Reihen differenzierbarer Funtionen,” Annals of Mathematics,316, No. 2, 521 (1935).

    Google Scholar 

  2. V. T. Pinkevich, “The order of the remainder of Fourier series of functions differentiable in the sense of Weyl,” Izv. AN SSSR,4, No. 5 (1940).

  3. S. M. Nikol'skii, “Asymptotic behavior of the remainder in approximating by Fejer sums functions satisfying Lipschitz condition,” Izv. AN SSSR, Ser. Matem.,4, No. 6 (1940).

  4. S. M. Nikol'skii, “Some approximation methods by trigonometric sums,” Izv. AN SSSR, Ser. Matem.,4, No. 6 (1940).

  5. S. M. Nikol'skii, “Asymptotic estimate of remainder in approximation by Fourier sums,” DAN SSSR,22, No. 6 (1941).

  6. S. M. Nikol'skii, “Approximation of periodic functions by trigonometric polynomials,” Trudy Matem. In-ta im. V. A. Steklova AN SSSR,15 (1945).

  7. A. V. Efimov, “Approximation of some classes of continuous functions by Fourier sums and Féjer sums,” Izv. AN SSSR, Ser. Matem.,22, No. 1 (1958).

  8. A. V. Efimov, “Approximation of continuous functions by Fourier sums,” UMN,14, No. 2 (1959).

  9. A. V. Efimov, “Approximation of functions with known continuity modulus by Fourier sums,” Izv. AN SSSR, Ser. Matem.,23, No. 1 (1959).

  10. A. V. Efimov, “Approximation of periodic functions by Vallee-Poussin sums. I,” Izv. AN SSSR, Ser. Matem.,23, No. 5 (1959).

  11. A. V. Efimov, “Linear summation methods of Fourier series for periodic functions,” DAN SSSR,131, No. 2 (1960).

  12. A. V. Efimov, “Approximation of continuous periodic functions by Fourier sums,” Izv. AN SSSR, Ser. Matem.,24, No. 2 (1960).

  13. A. V. Efimov, “Approximation of periodic functions by Vallee-Poussin sums. II,” Izv. AN SSSR, Ser. Matem.,24, No. 3 (1960).

  14. A. V. Efimov, “Linear approximation methods for some classes of continuous periodic functions,” Trudy Matem. In-ta im. V. A. Steklova AN SSSR,62 (1961).

  15. B. Nagy, “Sur une classe générale de procédés de sommation pour les series de Fourier,” Hungarica Acta Mathematica,1, No. 3 (1948).

  16. A. F. Timan, “Approximative properties of linear summation methods of Fourier series,” Izv. AN SSSR, Ser. Matem.,17, No. 2 (1953).

  17. S. A. Telyakovskii, “Approximation of differentiable functions by Vallee-Poussin sums,” DAN SSSR,121, No. 3 (1958).

  18. S. A. Telyakovskii, “Approximation of functions differentiable in the Weyl sense by Vallee-Poussin sums,” DAN SSSR,131, No. 2 (1960).

  19. S. A. Telyakovskii, “Approximation of differentiable functions by linear means of their Fourier series,” Izv. AN SSSR, Ser. Matem.,24, No. 2 (1960).

  20. S. A. Telyakovskii, “Norms of trigonometric polynomials and approximation of differentiable functions by linear means of their Fourier series. I,” Trudy Matem. In-ta im. V. A. Steklova AN SSSR,62 (1961).

  21. S. A. Telyakovskii, “Norms of trigonometric polynomials and approximation of differentiable functions by linear means of their Fourier series. II,” Izv. AN SSSR, Ser. Matem.,27, No. 2 (1963).

  22. S. A. Telyakovskii, “Integrability conditions of trigonometric series and their application to the study of linear summation methods of Fourier series,” Izv. AN SSSR, Ser. Matem.,28, No. 6 (1964).

  23. W. Rogosinski, “Über die Abschnitte trigonometrischer Reihen,” Mathematische Annalen,95 (1926).

  24. N. P. Korneichuk, Some Problems of Approximation of Periodic Functions by Trigonometric Polynomials, Thesis, Dnepropetrovsk (1959).

  25. N. P. Korneichuk, “Approximation of periodic functions satisfying the Lipschitz condition by Bernstein-Rogosinski sums,” DAN SSSR,125, No. 2 (1959).

  26. N. P. Korneichuk, Estimate of Approximations of Class Haby Trigonometric Polynomials; Investigation of Contemporary Problems of Constructive Theory of Functions [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  27. P. Turan, “On a trigonometrical sum,” Annales de la Soc. Polonaise de Mathématique,25, 155–161 (1952).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 22, No. 4, pp. 481–493, July–August, 1970.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dzyadyk, V.K., Gavrilyuk, V.T. & Stepanets, A.I. Exact upper bound for approximations on classes of differential periodic functions using Rogosinski polynomials. Ukr Math J 22, 411–421 (1970). https://doi.org/10.1007/BF01090766

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01090766

Keywords

Navigation