Inverse Polynomial Images are Always Sets of Minimal Logarithmic Capacity

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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 Padé-Approximation. The proofs are all based on the characterization theorems of Herbert Stahl.

Original languageEnglish
Pages (from-to)375-386
Number of pages12
JournalCOMPUTATIONAL METHODS AND FUNCTION THEORY
Volume16
Issue number3
DOIs
Publication statusPublished - 1 Sept 2016

Keywords

  • Inverse polynomial image
  • Minimal logarithmic capacity
  • Symmetry property

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