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Polynomials of the best uniform approximation to sgn(x) on two intervals

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Abstract

We describe polynomials of best uniform approximation to sgn(x) on the union of two intervals [−A,−1] ⊂ [1, B] in terms of special conformal mappings. This permits us to find the exact asymptotic behavior of the error in this approximation.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Alexandre Eremenko

  2. Abteilung Für Dynamische Systeme und Approximationstheorie, Johannes Kepler Universität Linz, A-4040, Linz, Austria

    Peter Yuditskii

Authors
  1. Alexandre Eremenko
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  2. Peter Yuditskii
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Corresponding author

Correspondence to Alexandre Eremenko.

Additional information

Supported by NSF grant DMS-0555279.

Supported by the Austrian Science Fund FWF, project no: P22025-N18.

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Eremenko, A., Yuditskii, P. Polynomials of the best uniform approximation to sgn(x) on two intervals. JAMA 114, 285–315 (2011). https://doi.org/10.1007/s11854-011-0018-7

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  • DOI: https://doi.org/10.1007/s11854-011-0018-7

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