Rates of convergence for holomorphic semigroups of finite shift
Complex Variables
2024-04-09 v2
Abstract
We study parabolic semigroups of finite shift in the unit disk with regard to the rate of convergence of their orbits to the Denjoy--Wolff point. We examine this rate in terms of Euclidean distance, hyperbolic distance and harmonic measure. In each case, we provide explicit examples to display the sharpness of the results. We further discuss the corresponding rates of convergence for parabolic semigroups of positive hyperbolic step and infinite shift.
Keywords
Cite
@article{arxiv.2403.06883,
title = {Rates of convergence for holomorphic semigroups of finite shift},
author = {Maria Kourou and Eleftherios K. Theodosiadis and Konstantinos Zarvalis},
journal= {arXiv preprint arXiv:2403.06883},
year = {2024}
}