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arXiv · 1408.1601

Polynomial and rational inequalities on Jordan arcs and domains

Sergei Kalmykov·Béla Nagy
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Abstract

In this paper we prove an asymptotically sharp Bernstein-type inequality for polynomials on analytic Jordan arcs. Also a general statement on mapping of a domain bounded by finitely many Jordan curves onto a complement to a system of the same number of arcs with rational function is presented here. This fact, as well as, Borwein-Erd\'elyi inequality for derivative of rational functions on the unit circle, Gonchar-Grigorjan estimate of the norm of holomorphic part of meromorphic functions and Totik's construction of fast decreasing polynomials play key roles in the proof of the main result.

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Sergei Kalmykov, Béla Nagy. 2014-08-07. Polynomial and rational inequalities on Jordan arcs and domains. https://doi.org/10.1016/j.jmaa.2015.05.022

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