Skip to main content
SpringerLink
Log in

On Saturation of Linear Summation Methods for Fourier Series in the Spaces \(S_\varphi ^p \)

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We consider the problem of the saturation of linear summation methods for Fourier series in the spaces \(S_\varphi ^p \), p > 0. We show that the saturation of a linear method and the saturation order are independent of the parameters X, ϕ, and p that define the space \(S_\varphi ^p \)(X).

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

Access this article

Log in via an institution

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. A. L. Shydlich, “Saturation of linear summation methods for Fourier series in the spaces S Pϕ ,” in: Theory of Approximation of Functions and Related Problems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002).

    Google Scholar 

  2. A. I. Stepanets, Approximation Characteristics of the Spaces S Pϕ [in Russian], Preprint 2002.2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002).

    Google Scholar 

  3. A. I. Stepanets, Approximation Characteristics of the Spaces S p[in Russian], Preprint 2001.2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2001).

    Google Scholar 

  4. A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  5. P. Butzer and R. Nessel, Fourier Analysis and Approximation, Vol. 1, Birkhäuser, Stuttgart (1971).

    Google Scholar 

  6. J. Favard, “Sur l'approximation des fonctions d'une variable reélle,” Ann. Harmon. Colloq. Int. CNRS, 15, 97–100 (1949).

    Google Scholar 

  7. G. Alexets, “Sur l'ordre de grandeur de l'approximation d'une fonction par les moyennes de la serie de Fourier,” Mat. Fis. Lapok., 48, 410–433 (1941).

    Google Scholar 

  8. A. Zygmund, “The approximation of functions by Fejér means,” Bull. Amer. Math. Soc., 51, No. 4, 274–278 (1945).

    Google Scholar 

  9. M. Zamansky, “Classes de saturation de certain procédés l'approximation des series Fourier des fonctions continues et applications a quelques problèmes l'approximation,” Ann. Sci. Ecole Norm. Supér., 66, No. 1, 19–93 (1949).

    Google Scholar 

  10. V. T. Gavrilyuk and A. I. Stepanets, “On the problem of saturation of linear methods,” Ukr. Mat. Zh., 43, No. 3, 291–308 (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. L. Shydlich

Authors
  1. A. L. Shydlich
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shydlich, A.L. On Saturation of Linear Summation Methods for Fourier Series in the Spaces \(S_\varphi ^p \) . Ukrainian Mathematical Journal 56, 166–172 (2004). https://doi.org/10.1023/B:UKMA.0000031712.84507.45

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:UKMA.0000031712.84507.45

Keywords

Search

Navigation