Constructive Approximation

, Volume 16, Issue 2, pp 261–281

Weighted Polynomial Approximation for Convex External Fields

  • Vilmos Totik

DOI: 10.1007/s003659910011

Cite this article as:
Totik, V. Constr. Approx. (2000) 16: 261. doi:10.1007/s003659910011


It is proven that if Q is convex and w(x)= exp(-Q(x)) is the corresponding weight, then every continuous function that vanishes outside the support of the extremal measure associated with w can be uniformly approximated by weighted polynomials of the form wnPn . This solves a problem of P. Borwein and E. B. Saff. Actually, a similar result is true locally for any parts of the extremal support where Q is convex.

Key words. Weighted polynomial approximation, Convex external fields. AMS Classification. 41A10. 

Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • Vilmos Totik
    • 1
    • 2
  1. 1.Bolyai Institute SzegedHungary
  2. 2.Department of MathematicsUniversity of South FloridaTampaUSA

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