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Asymptotics of Weighted Polynomials

  • M. v. Golitschek
  • G. G. Lorentz
  • Y. Makovoz
Conference paper
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 19)

Abstract

We survey recent developments in the theory of the weighted polynomials w(x) n P n (x), P n P n on a closed set A ⊂ R, with a continuous weight w(x) ≥ 0 on A. Important questions are: Where are the extreme points of the weighted polynomials distributed on A, in particular the alternation points of the weighted Chebyshev polynomials w n C w ,n ? Which continuous functions f on A are approximable by the weighted polynomials? How do the polynomials P n of weighted norm w n P n C (A) = 1 behave outside of A?

This is based on our own work (in particular, in the first two sections) and on work of Mhaskar and Saff, and others.

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • M. v. Golitschek
    • 1
  • G. G. Lorentz
    • 2
  • Y. Makovoz
    • 3
  1. 1.Inst. für Angewandte MathematikWÜrzburgGermany
  2. 2.Deptartment of Mathematics RLM 8-100University of TexasAustinUSA
  3. 3.Deptartment of MathematicsUniversity of Mass. at LowellLowellUSA

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