The Pólya-Chebotarev problem and inverse polynomial images

Klaus Schiefermayr

doi:10.1007/s10474-013-0353-5

The Pólya-Chebotarev problem and inverse polynomial images

Klaus Schiefermayr

Research Center Wels

Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

5 Zitate (Scopus)

Abstract

Consider the problem, usually called the Pólya-Chebotarev problem, of finding a continuum in the complex plane including some given points such that the logarithmic capacity of this continuum is minimal. We prove that each connected inverse image T^-1_n([-1,1]) of a polynomial T_n is always the solution of a certain Pólya-Chebotarev problem. By solving a nonlinear system of equations for the zeros of T²_n, we are able to construct polynomials T_n with a connected inverse image.

Originalsprache	Englisch
Seiten (von - bis)	80-94
Seitenumfang	15
Fachzeitschrift	Acta Mathematica Hungarica
Jahrgang	142
Ausgabenummer	1
DOIs	https://doi.org/10.1007/s10474-013-0353-5
Publikationsstatus	Veröffentlicht - Feb. 2014

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10.1007/s10474-013-0353-5

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The Pólya-Chebotarev problem and inverse polynomial images

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