Norm estimates for Chebyshev polynomials, I

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 monoto...

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Bibliographic Details
Published in:Journal of approximation theory 2021-05, Vol.265, p.105561, Article 105561
Main Authors: Schiefermayr, Klaus, Zinchenko, Maxim
Format: Article
Language:English
Subjects:
Chebyshev polynomials on a circular arc
Lower and upper bounds on Widom factors
Weighted Chebyshev polynomials
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Summary: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.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2021.105561