Semigroups versus evolution families in the Loewner theory

2009/07/24 by Filippo Bracci, Manuel D. Contreras, Bracci, Filippo +4
Mathematics · #30C80 #30D05 #34M15 #37L05 #Advanced Topics in Algebra #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.CV #math.DS #msc:30C80 #msc:30D05 #msc:34M15 #msc:37L05

paper · pdf · doi:10.48550/arxiv.0907.4324

19 pages

arxiv created 2009/07/24 · openalex publication_date 2009/07/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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