Polynomial and rational inequalities on Jordan arcs and domains

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....

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Bibliographic Details
Published in:arXiv.org 2015-06
Main Authors: Kalmykov, Sergei, Nagy, Béla
Format: Article
Language:English
Subjects:
Domains
Mapping
Mathematical analysis
Meromorphic functions
Polynomials
Rational functions
Online Access:Get full text
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Summary: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-Erdélyi 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1408.1601