Asymptotic upper bound for tangential speed of parabolic semigroups of holomorphic self-maps in the unit disc

Abstract

We show that the tangential speed of a parabolic semigroup of holomorphic self-maps in the unit disc is asymptotically bounded from above by (1/2)logt, proving a conjecture by Bracci. In order to show the proof we need a result of "asymptotical monotonicity" of the tangential speed for proper pairs of parabolic semigroups with positive hyperbolic step.

21 pages

References in corpus (1)

• Asymptotic monotonicity of the orthogonal speed and rate of convergence for semigroups of holomorphic self-maps of the unit disc

Cited by in corpus (1)

• Holomorphic semigroups of finite shift in the unit disc