Extremal polynomials on a Jordan arc
Abstract
Let $\Gamma$ be a $C^{2+}$ Jordan arc and let $\Gamma_0$ be the open arc which consists of interior points of $\Gamma$. We find concrete upper and lower bounds for the limit of Widom factors for $L_2(\mu)$ extremal polynomials on $\Gamma$ which was given in [18]. In addition, we show that the upper bound for the limit supremum of Widom factors for the weighted Chebyshev polynomials which was obtained in [18] can be improved once two normal derivatives of the Green function do not agree at one point $z\in \Gamma_0$. We also show that if $\Gamma_0$ is not analytic then we have improved upper bounds.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 DOI:
 10.48550/arXiv.2108.01798
 arXiv:
 arXiv:2108.01798
 Bibcode:
 2021arXiv210801798A
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Primary 41A17;
 Secondary 41A44;
 42C05;
 33C45