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

Research output: Contribution to journal › Article › peer-review

5 Citations (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.

Original language	English
Pages (from-to)	80-94
Number of pages	15
Journal	Acta Mathematica Hungarica
Volume	142
Issue number	1
DOIs	https://doi.org/10.1007/s10474-013-0353-5
Publication status	Published - Feb 2014

Keywords

30C10
41A21
analytic Jordan arc
inverse polynomial image
logarithmic capacity
Pólya-Chebotarev problem

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10.1007/s10474-013-0353-5

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abstract = "Consider the problem, usually called the P{\'o}lya-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-1n([-1,1]) of a polynomial Tn is always the solution of a certain P{\'o}lya-Chebotarev problem. By solving a nonlinear system of equations for the zeros of T2n, we are able to construct polynomials Tn with a connected inverse image.",

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KW - 30C10

KW - 41A21

KW - analytic Jordan arc

KW - inverse polynomial image

KW - logarithmic capacity

KW - Pólya-Chebotarev problem

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JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1

ER -

The Pólya-Chebotarev problem and inverse polynomial images

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Keywords

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