Open AccessOn boundary critical points for semigroups of analytic functions
Author(s) -
Manuel D. Contreras,
Santiago Díaz-Madrigal,
Ch. Pommerenke
Publication year - 2006
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14987
Subject(s) - mathematics , analytic function , unit disk , boundary (topology) , fixed point , mathematical analysis , infinitesimal , pure mathematics , global analytic function , boundary value problem , unit (ring theory) , mathematics education
We analyze the relationship between boundary fixed points of semigroups of analytic functions and boundary critical points of their infinitesimal generators. As a consequence, we show two new inequalities for analytic self-maps of the unit disk. The first one is about angular derivatives at fixed points of functions belonging to semigroups of analytic functions. The second one deals with angular derivatives at contact points of arbitrary analytic functions from the unit disk into itself.