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

Access to Document

10.1007/s10474-013-0353-5

Cite this

@article{053e905261304ac0a179d360e7dd31bb,

title = "The P{\'o}lya-Chebotarev problem and inverse polynomial images",

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.",

keywords = "30C10, 41A21, analytic Jordan arc, inverse polynomial image, logarithmic capacity, P{\'o}lya-Chebotarev problem",

author = "Klaus Schiefermayr",

year = "2014",

month = feb,

doi = "10.1007/s10474-013-0353-5",

language = "English",

volume = "142",

pages = "80--94",

journal = "Acta Mathematica Hungarica",

issn = "0236-5294",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - The Pólya-Chebotarev problem and inverse polynomial images

AU - Schiefermayr, Klaus

PY - 2014/2

Y1 - 2014/2

N2 - 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-1n([-1,1]) of a polynomial Tn is always the solution of a certain Pólya-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.

AB - 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-1n([-1,1]) of a polynomial Tn is always the solution of a certain Pólya-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.

KW - 30C10

KW - 41A21

KW - analytic Jordan arc

KW - inverse polynomial image

KW - logarithmic capacity

KW - Pólya-Chebotarev problem

UR - http://www.scopus.com/inward/record.url?scp=84895903400&partnerID=8YFLogxK

U2 - 10.1007/s10474-013-0353-5

DO - 10.1007/s10474-013-0353-5

M3 - Article

SN - 0236-5294

VL - 142

SP - 80

EP - 94

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1

ER -

The Pólya-Chebotarev problem and inverse polynomial images

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this