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Weighted Best Approximation by Polynomials

  • Feng Dai
  • Yuan Xu
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

The structure of spherical harmonics allows us to develop a theory of best polynomial approximation on the sphere based essentially on multipliers, which is, historically, the first approach in this direction. It turns out that the entire framework based on multipliers can be established more generally for h-spherical harmonics associated with reflection-invariant weight functions developed in Chap. 7, which leads to a theory of weighted best approximation by polynomials that we shall present in its full generality.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Feng Dai
    • 1
  • Yuan Xu
    • 2
  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA

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