Aleksandrov-Clark measures and semigroups of analytic functions in the unit disc

2007/01/29 by Filippo Bracci, Manuel D. Contreras, Bracci, Filippo +4 · 1 citation
Mathematics · #30D40 #30E20 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #advanced mathematical theories #math.CV #math.FA #msc:30D40 #msc:30E20

paper · pdf · doi:10.48550/arxiv.math/0701834

10 pages

arxiv created 2007/01/29 · openalex publication_date 2007/01/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 regular fixed point. The result is based on Alexandrov-Clark measures techniques. In particular we prove that the Alexandrov-Clark measure of (\v_t) at a boundary regular fixed points is differentiable (in the weak^∗-topology) with respect to t.

Cited by

• Boundary regular fixed points in Loewner theory

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