Rates of convergence for holomorphic semigroups of finite shift

2024/03/11 by Maria Kourou, Kourou, Maria, Eleftherios K. Theodosiadis +3 · 2 citations
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.06883

openalex publication_date 2024/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Extremal rate of convergence in discrete hyperbolic and parabolic dynamics
• Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators

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