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

• Dimitrios Betsakos ^[1] ; Manuel D. Contreras ^[2] ; Santiago Díaz-Madrigal ^[2]
  1. [1] Aristotle University of Thessaloniki

     Aristotle University of Thessaloniki

     Dimos Thessaloniki, Grecia

     
  2. [2] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 6, 2020, págs. 1659-1686
• Idioma: inglés
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• Resumen

  • Let {ϕt} be a semigroup of holomorphic self-maps of the unit disc D with Denjoy–Wolff point τ∈∂D. We study the rate of convergence of the semigroup to τ, that is, given z∈D¯¯¯¯, we discuss the behavior of |ϕt(z)−τ| as t goes to +∞.