Norm estimates for Chebyshev polynomials, I

Klaus Schiefermayr, Maxim Zinchenko

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we extend the sharp upper bound of Christiansen et al. (2017) and the sharp lower bound of Schiefermayr (2008) to the case of weighted Chebyshev polynomials on subsets of [−1,1] for the weight w(x)=1−x2. We then analyse the norm of Chebyshev polynomials on a circular arc, prove monotonicity of the corresponding Widom factors, find exact values of their supremum and infimum, and obtain a new proof for their limit.

Original languageEnglish
Article number105561
JournalJournal of Approximation Theory
Volume265
DOIs
Publication statusPublished - May 2021

Keywords

  • Chebyshev polynomials on a circular arc
  • Lower and upper bounds on Widom factors
  • Weighted Chebyshev polynomials

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