Infinitesimal generators associated with semigroups of linear fractional maps

2006/01/27 by Filippo Bracci, Manuel D. Contreras, Bracci, Filippo +3 · 1 citation
Mathematics · #30C99 #32A99 #Analytic and geometric function theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0601665

openalex publication_date 2006/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in \mathbb Cⁿ, n≥ 1. For the case n=1 we also completely describe the associated Koenigs function and we solve the embedding problem from a dynamical point of view, proving, among other things, that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear fractional maps if and only if it contains a linear fractional map for some positive time.

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• Local spectral theory for subordinated operators: the Cesàro operator and beyond

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