The Pólya–Chebotarev problem and inverse polynomial images

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 of a polynomial  is always the solution of a certain...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2014-02, Vol.142 (1), p.80-94
Main Author: Schiefermayr, Klaus
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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 of a polynomial  is always the solution of a certain Pólya–Chebotarev problem. By solving a nonlinear system of equations for the zeros of , we are able to construct polynomials with a connected inverse image.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-013-0353-5