Skip to main content
Log in

On the approximation in the mean of functions of the classes H[ω]L by de La Vallee Poussin sums

  • Brief Communications
  • 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. F. Timan, “Approximation properties of the linear methods for the summation of Fourier series,” Izv. Akad. Nauk SSSR, Ser. Mat.,17, No. 2 (1953).

  2. A. V. Efimov, “On the approximation of periodic functions by de La Vallee Poussin sums,” Izv. Akad. Nauk SSSR, Ser. Mat.,23, No. 5 (1959).

  3. A. V. Efimov, “On the approximation of periodic functions by de La Vallee Poussin sums, II,” Izv. Akad. Nauk SSSR, Ser. Mat.,24, No. 3 (1960).

  4. S. A. Telyakovskii, “On the approximation of differentiable functions by the linear averages of their Fourier series,” Izv. Akad. Nauk SSSR, Ser. Mat.,24, No. 2 (1960).

  5. A. N. Kolmogorov, “Zur Grossenordnung des Restgliedes Fourierscher Reihen differenzierbarer Funktionen,” Annals of Math.,36, No. 2 (1935).

  6. S. M. Nikol'skii, “The asymptotic estimate of the remainder in the approximation by Fourier series,” Dokl. Akad. Nauk SSSR,32, No. 6 (1941).

  7. S. M. Nikol'skii, “Approximation of periodic functions by trigonometric polynomials,” Trudy Mat. Inst. Steklov, Akad. Nauk SSSR,15 (1945).

  8. S. M. Nikol'skii, “The Fourier series of a function with a given modulus of continuity,” Dokl. Akad. Nauk SSSR,52, No. 3 (1946).

  9. A. V. Efimov, “On the approximation of some classes of continuous functions by Fourier sums and by Fejer sums,” Izv. Akad. Nauk SSSR, Ser. Mat.,22, No. 1 (1958).

  10. A. V. Efimov, “Approximation of functions with a given modulus of continuity by Fourier sums,” Izv. Akad. Nauk SSSR, Ser. Mat.,23, No. 1 (1959).

  11. S. A. Telyakovskii, “On norms of trigonometric polynomials and approximation of differentiable functions by linear averages of their Fourier series, I,” Trudy Mat. Inst. Steklov, Akad. Nauk SSSR,62 (1961).

  12. N. P. Korneichuk, “On the approximation of periodic functions which satisfy a Lipschitz condition by Bernstein-Rogosinski sums,” Dokl. Akad. Nauk SSSR,125, No. 2 (1959).

  13. V. K. Dzyadik, V. T. Gavrilyuk, and O. I. Stepanets, “The approximations of functions of Hölder classes by Rogosinski polynomials,” Dopovidi Akad. Nauk Ukrain. RSR, Ser. A, No. 3 (1969).

  14. V. K. Dzyadik, V. T. Gavrilyuk, and O. I. Stepanets, “The least upper bound of approximations on classes of differentiable periodic functions by means of Rogosinski polynomials,” Ukrainsk. Matem. Zh.,22, No. 4 (1970).

  15. V. T. Gavrilyuk and O. I. Stepanets, “The approximations of functions of Hölder classes by Bernstein sums,” Dopovidi Akad. Nauk Ukrainsk. RSR, Ser. A, No. 8 (1970).

  16. S. M. Nikol'skii, “Approximation of functions in the mean by trigonometric polynomials,” Izv. Akad. Nauk SSSR, Ser. Mat.,10, No. 3 (1946).

  17. S. B. Stechkin and S. A. Telyakovskii, “The approximation of differentiable functions in the L metric by trigonometric polynomials,” Trudy Mat. Inst. Steklov, Akad. Nauk SSSR,88 (1967).

  18. V. I. Berdyshev, “Approximation of periodic functions in the mean by Fourier sums,” Izv. Akad. Nauk SSSR, Ser. Mat.,29, No. 3 (1965).

  19. A. V. Efimov, “Linear methods for the approximation of continuous periodic functions,” Mat. Sb.,54, No. 1 (1961).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 24, No. 1, pp. 95–104, January–February, 1972.

The author considers it his pleasant obligation to express his sincere thanks to V. T. Gavrilyuk and A. I. Stepanets for their constant interest and helpful advice during the preparation of this paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Demchenko, A.G. On the approximation in the mean of functions of the classes H[ω]L by de La Vallee Poussin sums. Ukr Math J 24, 76–82 (1972). https://doi.org/10.1007/BF01089126

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01089126

Navigation