423 citations
- Centre National de la Recherche ScientifiqueFR17 papers
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4 papers · 1 filter
Semigroups versus evolution families in the Loewner theory
Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal
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 evol…
Evolution Families and the Loewner Equation II: complex hyperbolic manifolds
Filippo Bracci, Manuel D. Contreras, S. Diaz-Madrigal
We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, provi…
Iteration of the rational function z-1/z and a Hausdorff moment sequence
Christian Berg, Antonio J. Durán
In a previous paper we considered a positive function f, uniquely determined for s>0 by the requirements f(1)=1, log(1/f) is convex and the functional equation f(s)=psi(f(s+1)) wit…
Aleksandrov-Clark measures and semigroups of analytic functions in the unit disc
Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal
In this paper we prove a formula describing the infinitesimal generator of a continuous semigroup $(\v_t)$ of holomorphic self-maps of the unit disc with respect to a boundary regu…