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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.

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Authors and Affiliations

  1. Dipartimento Di Matematica, Università Di Roma “tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy

    Filippo Bracci

  2. Camino de los Descubrimientos, S/N Departamento de Matemática Aplicada II Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Sevilla, 41092, Spain

    Manuel D. Contreras & Santiago Díaz-Madrigal

Authors
  1. Filippo Bracci
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  2. Manuel D. Contreras
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  3. Santiago Díaz-Madrigal
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Corresponding author

Correspondence to Filippo Bracci.

Additional information

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

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Bracci, F., Contreras, M.D. & Díaz-Madrigal, S. Semigroups versus evolution families in the loewner theory. JAMA 115, 273–292 (2011). https://doi.org/10.1007/s11854-011-0030-y

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  • DOI: https://doi.org/10.1007/s11854-011-0030-y

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