Revista Matemática Iberoamericana


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Published online first: 2020-02-12
DOI: 10.4171/rmi/1179

On the rate of convergence of semigroups of holomorphic functions at the Denjoy–Wolff point

Dimitrios Betsakos[1], Manuel D. Contreras[2] and Santiago Díaz-Madrigal[3]

(1) Aristotle University of Thessaloniki, Greece
(2) Universidad de Sevilla, Spain
(3) Universidad de Sevilla, Spain

Let $\{\phi_t\}$ be a semigroup of holomorphic self-maps of the unit disc $\mathbb{D}$ with Denjoy–Wolff point $\tau\in \partial\mathbb{D}$. We study the rate of convergence of the semigroup to $\tau$, that is, given $z\in \overline{\mathbb{D}}$, we discuss the behavior of $|\phi_{t}(z)-\tau|$ as $t$ goes to $+\infty$.

Keywords: Semigroups of holomorphic functions, Denjoy–Wolff point, harmonic measure

Betsakos Dimitrios, Contreras Manuel, Díaz-Madrigal Santiago: On the rate of convergence of semigroups of holomorphic functions at the Denjoy–Wolff point. Rev. Mat. Iberoam. Electronically published on February 12, 2020. doi: 10.4171/rmi/1179 (to appear in print)