2024-11-122024-11-122025-02-01Cruz Zamorano, F.J. (2025). Characterization of finite shift via Herglotz’s representation. Journal of Mathematical Analysis and Applications, 542(1) (128883). https://doi.org/10.1016/j.jmaa.2024.128883.0022-247X1096-0813https://hdl.handle.net/11441/164363A 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, Díaz-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.application/pdf10 p.engAtribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Parabolic functionsComplex iterationFinite shiftRate of convergenceinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/j.jmaa.2024.128883