, Volume 115, Issue 1, pp 273-292
Date: 16 Nov 2011

Semigroups versus evolution families in the loewner theory

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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.

This work was partially supported by the Ministerio de Ciencia e Innovación and the European Union (FEDER), project MTM2009-14694-C02-02, La Consejería de Educación y Ciencia de la Junta de Andalucía and the European Science Foundation Research Networking Programme HCAA