On boundary critical points for semigroups of analytic functions

Authors

  • M. D. Contreras
  • S. Díaz-Madrigal
  • Ch. Pommerenke

DOI:

https://doi.org/10.7146/math.scand.a-14987

Abstract

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.

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Published

2006-03-01

How to Cite

Contreras, M. D., Díaz-Madrigal, S., & Pommerenke, C. (2006). On boundary critical points for semigroups of analytic functions. MATHEMATICA SCANDINAVICA, 98(1), 125–142. https://doi.org/10.7146/math.scand.a-14987

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Section

Articles