Harmonic Measures, Green Potentials and Semigroups of Holomorphic Functions

Harmonic Measures, Green Potentials and Semigroups of Holomorphic Functions

Let K be a compact subset of the unit disk D . We examine the asymptotic behavior of its trajectory under a semigroup of holomorphic self-maps ( ϕ t ) t ≥ 0 of D . More specifically, we obtain results concerning its geometric characteristics such as hyperbolic area, hyperbolic diameter, as well as p...

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Veröffentlicht in:Potential analysis 2020-02, Vol.52 (2), p.301-319
1. Verfasser: Kourou, Maria
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Asymptotic properties
Diameters
Functional Analysis
Geometry
Mathematical analysis
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
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Zusammenfassung:Let K be a compact subset of the unit disk D . We examine the asymptotic behavior of its trajectory under a semigroup of holomorphic self-maps ( ϕ t ) t ≥ 0 of D . More specifically, we obtain results concerning its geometric characteristics such as hyperbolic area, hyperbolic diameter, as well as potential theoretic quantities. Those are the harmonic measure of ϕ t ( K ), its equilibrium measure and its Green equilibrium potential.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-018-9748-9