Asymptotics of the best polynomial approximation of |χ|p and of the best laurent polynomial approximation of sgn(x) on two symmetric intervals

F. Nazarov, F. Peherstorfer, A. Volberg, P. Yuditskii

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4 Scopus citations

Abstract

We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best uniform polynomial approximation of |χ|p on two symmetric intervals. Note that, in addition, we get asymptotics for the polynomials themselves under a certain renormalization. Also, we solve a problem on asymptotics of the best approximation of sgn(x) on [-1,-a]∪[a,1] by Laurent polynomials.

Original languageEnglish
Pages (from-to)23-39
Number of pages17
JournalConstructive Approximation
Volume29
Issue number1
DOIs
StatePublished - Feb 2009
Externally publishedYes

Keywords

  • Bernstein constant
  • Chebyshev theorem
  • Conformal mapping
  • Hilbert transform

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