Skip to main content
Log in

Approximative characteristics of the isotropic classes of periodic functions of many variables

  • Published:
Ukrainian Mathematical Journal Aims and scope

Exact-order estimates are obtained for the best orthogonal trigonometric approximations of the Besov (B p r) and Nukol’skii (H p r) classes of periodic functions of many variables in the metric of L q , 1 ≤ p, q ≤ ∞. We also establish the orders of the best approximations of functions from the same classes in the spaces L 1 and L by trigonometric polynomials with the corresponding spectrum.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. O. V. Besov, “Investigation of a family of functional spaces in connection with the imbedding and extension theorems,” Trudy Mat. Inst. Akad Nauk SSSR, 60, 42–61 (1961).

    MATH  MathSciNet  Google Scholar 

  2. S. M. Nikol’skii, “Inequalities for finite-order entire functions and their application to the theory of differentiable functions of many variables,” Trudy Mat. Inst. Akad Nauk SSSR, 38, 244–278 (1951).

    Google Scholar 

  3. P. I. Lazorkin, “Generalized Hölder spaces B p (r) and their relationship to the Sobolev spaces L p (r),” Sib. Mat. Zh., 9, No. 5, 1127–1152 (1968).

    Google Scholar 

  4. A. S. Romanyuk, “Approximation of the classes of periodic functions of many variables,” Mat. Zametki, 70, No. 1, 109–121 (2002).

    MathSciNet  Google Scholar 

  5. A. S. Romanyuk, “Bilinear and trigonometric approximations of the Besov classes L p (r) of periodic functions of many variables,” Izv. Ros. Akad. Nauk, Ser. Mat., 70, No. 2, 69–98 (2006).

    MathSciNet  Google Scholar 

  6. S. B. Stechkin, “On the absolute convergence of orthogonal series,” Dokl. Akad. Nauk SSSR, 102, No. 2, 37-40 (1955).

    MATH  MathSciNet  Google Scholar 

  7. A. S. Romanyuk, “Best M-term trigonometric approximations of the Besov classes of periodic functions of many variables,” Izv. Ros. Akad. Nauk., Ser. Mat., 67, No. 2, 61–100 (2003).

    MathSciNet  Google Scholar 

  8. R. A. de Vore and V. N. Temlyakov, “Nonlinear approximation by trigonometric sums,” J. Fourier Anal. Appl., 2, No. 1, 29–48 (1995).

    Article  MathSciNet  Google Scholar 

  9. D. Jackson, “Certain problems of closest approximation,” Bull. Amer. Math. Soc., 39, No. 12, 889–906 (1933).

    Article  MathSciNet  Google Scholar 

  10. N. P. Korneichuk, Exact Constants in the Approximation Theory [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  11. V. N. Temlyakov, “Approximation of functions with bounded mixed derivative,” Trudy Mat. Inst. Akad. Nauk SSSR, 178, 1–112 (1986).

    MathSciNet  Google Scholar 

  12. V. N. Temlyakov, “Greedy algorithm and m-term trigonometric approximation,” Constr. Appr., 14, 569–587 (1998).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 4, pp. 513–523, April, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Romanyuk, A.S. Approximative characteristics of the isotropic classes of periodic functions of many variables. Ukr Math J 61, 613–626 (2009). https://doi.org/10.1007/s11253-009-0232-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-009-0232-y

Keywords

Navigation