On the uniform approximation of holomorphic functions on convex sets by means of interpolation polynomials

  • Thomas Kövari
Convergence Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)


The principal aim of this paper is to give an explicit construction for a sequence of polynomials that interpolates the function f on a given system of nodes and also converges to f uniformly. The functions we are able to approximate in this manner are continuous on the compact convex set K, and holomorphic in the interior of K.


Uniform Approximation Jordan Curve Interpolation Polynomial Jordan Domain Regular Node 
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  1. 1.
    J.M. Anderson and J. G. Clunie: "Isomorphisms of the Disc Algebra and Inverse Faber sets" (to be published).Google Scholar
  2. 2.
    J.E. Andersson: Dissertation, Göteborg 1975.Google Scholar
  3. 3.
    T. Kövari and Ch. Pommerenke: "On Faber polynomials and Faber expansions", Math. Zeit., 99(1967), 193–206.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    T. Kövari, "On the uniform approximation of analytic functions by means of interpolation polynomials”, Commentarii Math. Helv. 43(1968), 212–216.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    T. Kövari and Ch. Pommerenke, "On the distribution of Fekete points", Mathematika, 15(1968), 70–75.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    T. Kövari, "On the distribution of Fekete points II", Mathematika, 18(1971), 40–49.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    T. Kövari, "On the order of polynomial approximation for closed Jordan domains", Journ. of Approx. Theory 5(1972), 362–373.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Thomas Kövari
    • 1
  1. 1.Department of MathematicsImperial CollegeLondon

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