Inverse Polynomial Images are Always Sets of Minimal Logarithmic Capacity

In this paper, we prove that each inverse polynomial image (that is, each inverse image of an interval with respect to a polynomial mapping) is a set of minimal logarithmic capacity in a certain sense. Such sets play an important role in the theory of Padé-Approximation. The proofs are all based on...

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Bibliographic Details
Published in:Computational methods and function theory 2016-09, Vol.16 (3), p.375-386
Main Author: Schiefermayr, Klaus
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
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Summary:In this paper, we prove that each inverse polynomial image (that is, each inverse image of an interval with respect to a polynomial mapping) is a set of minimal logarithmic capacity in a certain sense. Such sets play an important role in the theory of Padé-Approximation. The proofs are all based on the characterization theorems of Herbert Stahl.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-015-0143-x