Inverse Polynomial Images are Always Sets of Minimal Logarithmic Capacity

Klaus Schiefermayr

doi:10.1007/s40315-015-0143-x

Inverse Polynomial Images are Always Sets of Minimal Logarithmic Capacity

Klaus Schiefermayr^*

^*Korrespondierende/r Autor/-in für diese Arbeit

Research Center Wels

Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

Abstract

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.

Originalsprache	Englisch
Seiten (von - bis)	375-386
Seitenumfang	12
Fachzeitschrift	COMPUTATIONAL METHODS AND FUNCTION THEORY
Jahrgang	16
Ausgabenummer	3
DOIs	https://doi.org/10.1007/s40315-015-0143-x https://doi.org/10.1007/s40315-015-0143-x
Publikationsstatus	Veröffentlicht - 1 Sep. 2016

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abstract = "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 Pad{\'e}-Approximation. The proofs are all based on the characterization theorems of Herbert Stahl.",

keywords = "Inverse polynomial image, Minimal logarithmic capacity, Symmetry property",

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AB - 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.

KW - Inverse polynomial image

KW - Minimal logarithmic capacity

KW - Symmetry property

UR - https://www.scopus.com/pages/publications/84982806674

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Inverse Polynomial Images are Always Sets of Minimal Logarithmic Capacity

Abstract

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