Skip to main content
SpringerLink
Log in

On the fixing of values of sequences of seminorms

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Theorems on the fixing of values of sequences of continuous seminorms on certain sets in Banach spaces are proved, enabling one to obtain new results on the asymptotic behavior of approximations of individual functions and on the convergence of interpolation processes on classes of functions.

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

Literature cited

  1. N. P. Korneichuk, “S. M. Nikol'skii and the development of the study of the theory of approximation of functions in the USSR,” Us. Mat. Nauk,40, No. 5, 71–131 (1985).

    Google Scholar 

  2. W. Dickmeis, R. J. Nessel, and E. van Wickeren, “Quantitative extension of the uniform boundedness principle,” Jahresber. Deutsch. Math. Ver.,89, No. 3, 106–134 (1987).

    Google Scholar 

  3. E. van Wickeren, “A Baire approach to quantitative resonance principles,” Numer. Anal. Optimiz.,9, Nos. 1 and 2, 147–180 (1987).

    Google Scholar 

  4. O. V. Davydov, Asymptotic Behavior of Best Approximations to Functions and Functionals [in Russian], Diss. Kand. Fiz.-Mat. Nauk., Dnepropetrovsk (1987).

    Google Scholar 

  5. O. V. Davydov, “Asymptotic behavior of best approximations of individual functions in the classes WrHω in the Lp metric,” Dokl. Akad. Nauk SSSR,306, No. 4, 777–781 (1989).

    Google Scholar 

  6. J. Peetre, “Nouvelles propriétés d'espaces d'interpolation,” C. R. Acad. Sci. Paris,256, 1424–1426 (1963).

    Google Scholar 

  7. O. V. Davydov, “Fixing of values of sequences of seminorms on sets defined by a majorant of a best approximation,” Approximation of Functions by Polynomials and Splines and the Summation of Series [in Russian], Izd. Dnepropetr. Univ., Dnepropetrovsk (1990), pp. 18–24.

    Google Scholar 

  8. N. P. Korneichuk, Extremal Problems in the Theory of Approximation [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  9. O. V. Davydov, “Approximation of individual functions by Fourier sums and their means,” in: Approximation of Functions by Polynomials and Splines and Summation of Series [in Russian], Izd. Dnepropetr. Univ., Dnepropetrovsk (1988), pp. 20–23.

    Google Scholar 

  10. O. V. Davydov, “Asymptotic behavior of approximations of individual functions and convergence of interpolation processes,” in: Theory of Functions and Approximations, Memoirs of the 4th Saratov Winter School (Jan. 25–Feb. 5, 1988), Part 2 [in Russian], Izd. Saratov, Univ., Saratov (1990), pp. 79–81.

    Google Scholar 

  11. O. V. Davydov, “Convergence of Lagrange interpolation processes in classes of differentiable functions,” Izv. Vuzov., Mat., No. 4, 74–77 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dnepropetrovsk University, USSR

    O. V. Davydov

Authors
  1. O. V. Davydov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 467–474, April, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Davydov, O.V. On the fixing of values of sequences of seminorms. Ukr Math J 44, 409–416 (1992). https://doi.org/10.1007/BF01064873

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01064873

Keywords

Search

Navigation