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arXiv · 2108.01798

Extremal polynomials on a Jordan arc

Gökalp Alpan
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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.

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Gökalp Alpan. 2021-08-04. Extremal polynomials on a Jordan arc. https://arxiv.org/abs/2108.01798

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