TY - JOUR
T1 - The Pólya-Chebotarev problem and inverse polynomial images
AU - Schiefermayr, Klaus
N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
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 -