Skip to main content

Advertisement

Log in

Approximation of cauchy-type integrals in Jordan domains

  • Published:
Ukrainian Mathematical Journal Aims and scope

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The concept of a generalized ψ-derivative of a function of a complex variable is introduced and applied to classify functions analytic in Jordan domains. The approximations of functions from the classes introduced by this procedure are studied by using algebraic polynomials constructed on the basis of the Faber polynomials after the summation of Faber series. Analogs of the author's results are obtained for the classesL Ψβ

in the periodic case.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. K. Dzyadyk,Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. V. I. Smirnov and N. A. Lebedev,The Constructive Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1964).

    Google Scholar 

  3. P. K. Suetin,Series in the Faber Polynomials [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  4. P. M. Tamrazov,Smoothness and Polynomial Approximations [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

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

    Google Scholar 

  6. A. I. Stepanets, “On the Lebesgue inequality on the classes of (ψ, β)-differentiable functions,”Ukr. Mat. Zh.,41, No. 5, 499–510 (1989).

    Google Scholar 

  7. A. I. Stepanets, “Classes of functions defined on the real axis and their approximations by entire functions. I,”Ukr. Mat. Zh.,42, No. 1, 102–112 (1990).

    Google Scholar 

  8. A. I. Stepanets, “Classes of functions defined on the real axis and their approximations by entire functions. II,”Ukr. Mat. Zh.,42, No. 2, 210–222 (1990).

    Google Scholar 

  9. A. Zygmund,Trigonometric Series, Vol. 2, Cambridge University Press, Cambridge (1959).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 6, pp. 809–833, June, 1993.

This paper was supported by the Ukrainian State Committee for Science and Technology.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stepanets, A.I. Approximation of cauchy-type integrals in Jordan domains. Ukr Math J 45, 890–917 (1993). https://doi.org/10.1007/BF01061441

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01061441

Keywords

Navigation