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On the Denseness of Weighted Incomplete Approximations

  • Peter Borwein
  • E. B. Saff
Conference paper
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 19)

Abstract

For a given weight function w(x) on an interval [a, b], we study the generalized Weierstrass problem of determining the class of functions fC[a, b] that are uniform limits of weighted polynomials of the form w n (x)p n (x) 1 , where p n is a polynomial of degree at most n. For a special class of weights, we show that the problem can be solved by knowing the denseness interval of the alternation points for the associated Chebyshev polynomials.

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Peter Borwein
    • 1
  • E. B. Saff
    • 2
  1. 1.Department of MathematicsDalhaousie UniversityHalifaxCanada
  2. 2.Institute for Constructive Math. Department of MathematicsUniversity of South FloridaTampaUSA

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