Characterization of finite shift via Herglotz's representation
Francisco J. Cruz-Zamorano
TL;DR
This paper provides a comprehensive characterization of finite shift parabolic self-maps using Herglotz's representation, leading to improved understanding of their convergence behavior to the Denjoy-Wolff point.
Contribution
It offers a complete characterization of finite shift parabolic self-maps via Herglotz's representation, enhancing previous results and convergence rate estimates.
Findings
Complete characterization of finite shift parabolic self-maps.
Improved convergence rate estimates to the Denjoy-Wolff point.
Refinement of previous results by Contreras, Días-Madrigal, and Pommerenke.
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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Taxonomy
TopicsMatrix Theory and Algorithms · Approximation Theory and Sequence Spaces