{"title":"Characterization of finite shift via Herglotz's representation","authors":"Francisco J. Cruz-Zamorano","doi":"arxiv-2407.10664","DOIUrl":null,"url":null,"abstract":"A complete characterization of parabolic self-maps of finite shift is given\nin terms of their Herglotz's representation. This improves a previous result\ndue to Contreras, D\\'iaz-Madrigal, and Pommerenke. We also derive some\nconsequences for the rate of convergence of these functions to their\nDenjoy-Wolff point, improving a related result of Kourou, Theodosiadis, and\nZarvalis for the continuous setting.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.10664","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.