PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
March 21, 2026Bulletin of the London Mathematical Society0 citationsOpen Access

Symmetrization and the rate of convergence of semigroups of holomorphic functions

View Full Paper
DBDimitrios BetsakosACArgyrios Christodoulou

Key Points

  • The research investigates how symmetrization affects the convergence rates of semigroups of holomorphic functions.
  • Analyzed semigroups of holomorphic self-maps in the unit disk.
  • Defined the Koenigs domain and Denjoy-Wolff point for each semigroup.
  • Applied Steiner symmetrization in relation to the real axis.
  • Utilized harmonic measure as a key analytical tool.
  • Convergence rate of the symmetrized semigroup is slower than that of the original semigroup.
  • The findings suggest a significant influence of symmetrization on convergence rates.

Abstract

Abstract Let , , be a semigroup of holomorphic self‐maps of the unit disk . Let be its Koenigs domain and be its Denjoy–Wolff point. Suppose that and let be the Steiner symmetrization of with respect to the real axis. Consider the semigroup with Koenigs domain and let be its Denjoy–Wolff point. We show that, up to a multiplicative constant, the rate of convergence of is slower than that of ; that is, for every , . The main tool for the proof is the harmonic measure.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Betsakos et al. (2026) studied this question.

synapsesocial.com/papers/69be37f16e48c4981c677ecahttps://doi.org/10.1112/blms.70337
Ask AI
Helpful
Bookmark
Share
View Full Paper