Fixed points of the Ruelle-Thurston operator and the Cauchy transform

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Abstract

We give necessary and sufficient conditions for a function in a naturally appearing function space to be a fixed point of the Ruelle-Thurston operator associated to a rational function (see Lemma 2.1). The proof uses essentially a 2020 paper of the author. As an immediate consequence, in Theorem 1 and Lemma 2.2 we revisit Theorem 1 and Lemma 5.2 of Levin (2014).

Original languageAmerican English
Pages (from-to)49-67
Number of pages19
JournalFundamenta Mathematicae
Volume254
Issue number1
DOIs
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 Instytut Matematyczny PAN.

Keywords

  • Cauchy transform
  • Herman rings
  • Rational approximation
  • Ruelle-Thurston pushforward operator
  • Transversality

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