Journal d’Analyse Mathématique

, Volume 96, Issue 1, pp 191–223 | Cite as

Sharpening of Hilbert’s lemniscate theorem

  • Béla Nagy
  • Vilmos Totik


In this paper, we extend Hilbert’s lemniscate theorem to touching systems of curves. The result allows finding sharp constants in Bernstein type inequalities.


Green Line Tangent Line Normal Derivative Jordan Curve Level Line 
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]
    L. V. Ahlfors,Conformal Invariants, McGraw-Hill, New York, 1973.zbMATHGoogle Scholar
  2. [2]
    W. Blaschke,Kreis und Kugel, de Gruyter, Berlin, 1956.zbMATHGoogle Scholar
  3. [3]
    R. A. de Vore and G. G. Lorentz,Contructive Approximation, Springer-Verlag, New York, 1993.Google Scholar
  4. [4]
    B. Nagy,Bernstein’s inequality on lemniscates, J. Math. Anal. Appl.301 (2005), 449–456.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    C. H. Pommerenke,Boundary Behavior of Conformal Mappings, Springer-Verlag, Berlin, Heidelberg, New York, 1992.Google Scholar
  6. [6]
    T. Ransford,Potential Theory in the Complex Plane, Cambridge University Press, Cambridge, 1995.zbMATHGoogle Scholar
  7. [7]
    E. B. Saff and V. Totik,Logarithmic Potentials with External Fields, Springer-Verlag, Berlin, Heidelberg, New York, 1997.zbMATHGoogle Scholar
  8. [8]
    M. Tsuji,Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959.zbMATHGoogle Scholar

Copyright information

© The Hebrew University Magnes Press 2005

Authors and Affiliations

  • Béla Nagy
    • 1
  • Vilmos Totik
    • 1
    • 2
  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary
  2. 2.Department of MathematicsUniversity of South FloridaTampaUSA

Personalised recommendations