# 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 language English 105561 Journal of Approximation Theory 265 https://doi.org/10.1016/j.jat.2021.105561 Published - May 2021

## Keywords

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