Norm estimates for Chebyshev polynomials, I

JOURNAL OF APPROXIMATION THEORY

卷:265

Article

Schiefermayr, Klaus¹  Zinchenko, Maxim² 

[1] Univ Appl Sci Upper Austria, Campus Wels, Wels, Austria

[2] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87131 USA

关键词: Weighted Chebyshev polynomials;    Chebyshev polynomials on a circular arc;    Lower and upper bounds on;    Widom factors;   

DOI  :  10.1016/j.jat.2021.105561

来源: Elsevier

【 摘 要 】

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) = root 1 - x(2). 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. (C) 2021 The Authors. Published by Elsevier Inc.

【 授权许可】

Free