Abstract:
In this paper we study linear-fractional models for one-parameter semigroups of holomorphic mappings via Schröder's and Abel's functional equation. By using some limit schemes in the spirit of Kœnigs to solve those equation, we obtain new results on the asymptotic behavior of one-parameter semigroups having a boundary Denjoy–Wolff fixed point. In addition, we establish infinitisimal versions of the Burns-Krantz rigidity theorem for semigroups and
their generators.
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