• The Pólya–Chebotarev prob...

Treffer: The Pólya–Chebotarev problem and inverse polynomial images: The Pólya-Chebotarev problem and inverse polynomial images

Title:
The Pólya–Chebotarev problem and inverse polynomial images: The Pólya-Chebotarev problem and inverse polynomial images
Authors:
Klaus Schiefermayr
Source:
Acta Mathematica Hungarica. 142:80-94
Publication Status:
Preprint
Publisher Information:
Springer Science and Business Media LLC, 2013.
Publication Year:
2013
Subject Terms:
analytic Jordan arc, inverse polynomial image, Mathematics - Complex Variables, Polynomials and rational functions of one complex variable, the Green's function, FOS: Mathematics, Pólya-Chebotarev problem, Complex Variables (math.CV), 0101 mathematics, 16. Peace & justice, Padé approximation, logarithmic capacity, 01 natural sciences
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1588-2632
0236-5294
DOI:
10.1007/s10474-013-0353-5
DOI:
10.48550/arxiv.1306.6170
Access URL:
http://arxiv.org/pdf/1306.6170
http://arxiv.org/abs/1306.6170
https://zbmath.org/6270607
https://doi.org/10.1007/s10474-013-0353-5
https://link.springer.com/article/10.1007/s10474-013-0353-5
https://rd.springer.com/article/10.1007/s10474-013-0353-5
Rights:
Springer TDM
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....a483e85f1167de52e11c0a2cce8ef3e9
Database:
OpenAIRE

Weitere Informationen

Consider the problem, usually called the P��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 $\T_n^{-1}([-1,1])$ of a polynomial $\T_n$ is always the solution of a certain P��lya-Chebotarev problem. By solving a nonlinear system of equations for the zeros of $\T_n^2-1$, we are able to construct polynomials $\T_n$ with a connected inverse image.