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arXiv · 0907.4324

Semigroups versus evolution families in the Loewner theory

Filippo Bracci·Manuel D. Contreras·Santiago Diaz-Madrigal
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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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Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal. 2009-07-24. Semigroups versus evolution families in the Loewner theory. https://arxiv.org/abs/0907.4324

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