Symmetrization and the rate of convergence of semigroups of holomorphic functions

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.