Mathematical Notes

, Volume 59, Issue 5, pp 498–506 | Cite as

Best Hausdorff approximations by algebraic polynomials and porosity

  • A. I. Ermakov


For anyb ∈ (a, a′), a sharp lower bound for the coefficient ofv-uniformity of the set of discontinuity points of a functionf on the interval (−b, b) is obtained.


Porosity Discontinuity Point Algebraic Polynomial Hausdorff Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bl. Sendov,Hausdorff Approximations [in Russian], Bolgar. Akad. Nauk, Sofia (1979).Google Scholar
  2. 2.
    E. P. Dolzhenko and E. A. Sevast'yanov, “The dependence of properties of functions on the rate of their approximation by polynomials,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],42, 469–470 (1978).Google Scholar
  3. 3.
    E. P. Dolzhenko and E. A. Sevast'yanov, “Approximations of functions in the Hausdorff metric,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],226, No. 4, 768–770 (1976).MathSciNetGoogle Scholar
  4. 4.
    P. P. Petrushev and Sp. Tashev, “Some inverse theorems in the Hausdorff metric,”C. R. Acad. Bulgare Sci.,29, 1721–1724 (1976).MathSciNetGoogle Scholar
  5. 5.
    A. I. Ermakov, “Best Hausdorff approximations by algebraic polynomials, and the continuity of a function,”Mat. Zametki [Math. Notes],28, No. 6, 843–858 (1980).MATHMathSciNetGoogle Scholar
  6. 6.
    A. P. Petukhov, “Dependence of the properties of the set of points of discontinuity of a function on the rate of its Hausdorff polynomial approximations,”Mat. Sb. [Math. USSR-Sb.],180, No. 7, 969–988 (1989).MATHGoogle Scholar
  7. 7.
    E. P. Dolzhenko, “Boundary properties of arbitrary functions,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],31, No. 1, 3–14 (1967).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • A. I. Ermakov
    • 1
  1. 1.East-Ukrainian State UniversityUkraine

Personalised recommendations