Semigroups of holomorphic functions and condenser capacity

Dimitrios Betsakos, Georgios Kelgiannis, Maria Kourou, Stamatis Pouliasis

Research output: Contribution to journalArticle

Abstract

Suppose (ϕt)t≥0 is a semigroup of holomorphic functions in the unit disk D with Denjoy–Wolff point τ= 1. Suppose K is a compact subset of D. We prove that the capacity of the condenser (D, ϕt(K)) is a decreasing function of t. Moreover, we study its asymptotic behavior as t→ + ∞ in relation with the type of the semigroup.

Original languageEnglish
Article number8
JournalAnalysis and Mathematical Physics
Volume10
Issue number1
DOIs
StatePublished - Mar 1 2020

Keywords

  • Condenser capacity
  • Green capacity
  • Hyperbolic semigroup
  • Koenigs function
  • Parabolic semigroup
  • Semigroup of holomorphic functions

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