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).
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- Cauchy transform
- Herman rings
- Rational approximation
- Ruelle-Thurston pushforward operator