Skip to main content
Log in

Best m-term approximation of the classes\( B_{\infty, \theta }^r \) of functions of many variables by polynomials in the haar system

  • Published:
Ukrainian Mathematical Journal Aims and scope

We obtain an exact-order estimate for the best m-term approximation of the classes \( B_{\infty, \theta }^r \) of periodic functions of many variables by polynomials in the Haar system in the metric of the space L q , 1 < q < ∞.

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. V. N. Temlyakov, “Nonlinear methods of approximation,” Found. Comput. Math., 3, No. 1, 33–107 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. S. Romanyuk, “The 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 

  3. A. S. Romanyuk and V. S. Romanyuk, “Asymptotic estimates for the best trigonometric and bilinear approximations of classes of functions of several variables,” Ukr. Mat. Zh., 62, No. 4, 536–551 (2010); English translation: Ukr. Math. J., 62, No. 4, 612–629 (2010).

    Article  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  5. B. S. Kashin and A. A. Saakyan, Orthogonal Series [in Russian], AFTs, Moscow (1999).

    Google Scholar 

  6. V. N. Temlyakov, “The best m-term approximation and greedy algorithms,” Adv. Comput. Math., 8, No. 3, 249–265 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  7. V. N. Temlyakov, “Nonlinear m-term approximation with regard to the multivariate Haar system,” East J. Approxim., 4, No. 1, 87–106 (1998).

    MathSciNet  MATH  Google Scholar 

  8. A. V. Andrianov and V. N. Temlyakov, “Best m-term approximation of functions from classes \( M\,W_{q,a}^r \),” Approxim. Theory, 1, 7–14 (1998).

    MathSciNet  Google Scholar 

  9. A.V. Andrianov, “Approximation of functions from the classes \( M\,H_p^r \) by the Haar polynomials,” Mat. Zametki, 66, No. 3, 323–335 (1999).

    MathSciNet  Google Scholar 

  10. P. Oswald, “On N-term approximations in the Haar system in H s-norms,” Sovr. Mat. Fund. Napr., 25, 106–125 (2007).

    Google Scholar 

  11. S. A. Stasyuk, “Approximation of functions of many variables from the classes \( H_p^\Omega \) by polynomials in the Haar system,” Anal. Math., 35, No. 4, 257–271 (2009).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 4, pp. 549–555, April, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stasyuk, S.A. Best m-term approximation of the classes\( B_{\infty, \theta }^r \) of functions of many variables by polynomials in the haar system. Ukr Math J 63, 638–645 (2011). https://doi.org/10.1007/s11253-011-0530-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-011-0530-z

Keywords

Navigation