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arXiv · 2407.10664

Characterization of finite shift via Herglotz's representation

Francisco J. Cruz-Zamorano
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Abstract

A complete characterization of parabolic self-maps of finite shift is given in terms of their Herglotz's representation. This improves a previous result due to Contreras, D\'iaz-Madrigal, and Pommerenke. We also derive some consequences for the rate of convergence of these functions to their Denjoy-Wolff point, improving a related result of Kourou, Theodosiadis, and Zarvalis for the continuous setting.

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Francisco J. Cruz-Zamorano. 2024-07-15. Characterization of finite shift via Herglotz's representation. https://arxiv.org/abs/2407.10664

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