Polynomial and rational inequalities on analytic Jordan arcs and domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

Kalmykov, S. I.^1,2,3  Nagy, B.⁴ 

[1] FEBRAS, Inst Appl Math, Vladivostok 690041, Russia

[2] Far Eastern Fed Univ, Vladivostok 690950, Russia

[3] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

[4] Univ Szeged, Bolyai Inst, MTA SZTE Anal & Stochast Res Grp, H-6720 Szeged, Hungary

关键词: Polynomials;    Rational functions;    Bernstein-type inequalities;    Conformal mappings;   

DOI  :  10.1016/j.jmaa.2015.05.022

来源: Elsevier

【 摘 要 】

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-Erdelyi 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. (C) 2015 Published by Elsevier Inc.

【 授权许可】

Free