JournalsrmiVol. 36, No. 6pp. 1659–1686

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

  • Dimitrios Betsakos

    Aristotle University of Thessaloniki, Greece
  • Manuel D. Contreras

    Universidad de Sevilla, Spain
  • Santiago Díaz-Madrigal

    Universidad de Sevilla, Spain
On the rate of convergence of semigroups of holomorphic functions at the Denjoy–Wolff point cover

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Abstract

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

Cite this article

Dimitrios Betsakos, Manuel D. Contreras, Santiago Díaz-Madrigal, On the rate of convergence of semigroups of holomorphic functions at the Denjoy–Wolff point. Rev. Mat. Iberoam. 36 (2020), no. 6, pp. 1659–1686

DOI 10.4171/RMI/1179