Journal d'Analyse Mathématique

, Volume 115, Issue 1, pp 273–292 | Cite as

Semigroups versus evolution families in the loewner theory

  • Filippo Bracci
  • Manuel D. Contreras
  • Santiago Díaz-Madrigal
Article

Abstract

We show that an evolution family of the unit disc is commuting if and only if the associated Herglotz vector field has separated variables. This is the case if and only if the evolution family comes from a semigroup of holomorphic self-maps of the disc.

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Copyright information

© Hebrew University Magnes Press 2011

Authors and Affiliations

  • Filippo Bracci
    • 1
  • Manuel D. Contreras
    • 2
  • Santiago Díaz-Madrigal
    • 2
  1. 1.Dipartimento Di MatematicaUniversità Di Roma “tor Vergata”RomaItaly
  2. 2.Camino de los Descubrimientos, S/N Departamento de Matemática Aplicada II Escuela Técnica Superior de IngenieríaUniversidad de SevillaSevillaSpain

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