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^*

^*Corresponding author for this work

Research Center Wels

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	375-386
Number of pages	12
Journal	COMPUTATIONAL METHODS AND FUNCTION THEORY
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/s40315-015-0143-x https://doi.org/10.1007/s40315-015-0143-x
Publication status	Published - 1 Sept 2016

Keywords

Inverse polynomial image
Minimal logarithmic capacity
Symmetry property

Access to Document

Cite this

@article{d9e241a018204026a98cace1a30ab815,

title = "Inverse Polynomial Images are Always Sets of Minimal Logarithmic Capacity",

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",

author = "Klaus Schiefermayr",

note = "Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",

year = "2016",

month = sep,

day = "1",

doi = "10.1007/s40315-015-0143-x",

language = "English",

volume = "16",

pages = "375--386",

journal = "COMPUTATIONAL METHODS AND FUNCTION THEORY",

publisher = "Springer",

number = "3",

}

TY - JOUR

T1 - Inverse Polynomial Images are Always Sets of Minimal Logarithmic Capacity

AU - Schiefermayr, Klaus

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

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

U2 - 10.1007/s40315-015-0143-x

DO - 10.1007/s40315-015-0143-x

M3 - Article

VL - 16

SP - 375

EP - 386

JO - COMPUTATIONAL METHODS AND FUNCTION THEORY

JF - COMPUTATIONAL METHODS AND FUNCTION THEORY

IS - 3

ER -

Inverse Polynomial Images are Always Sets of Minimal Logarithmic Capacity

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this