Discrete and Continuous Signals: Analysis, Information and Applications

Domains of univalence for classes of bounded holomorphic functions

16 Dec 2023, 10:00

50m

St. Petersburg University, MCS faculty

Speaker

Aleksei Solodov (Moscow state university)

Description

The problem of finding domains of univalence for classes of holomorphic self-mappings of the disc is concidered. In 1926, E. Landau found sharp radius of the disc of univalence for the class of such mappings with a given value of derivative at the inner fixed point.
In 2017, V.V. Goryainov discovered the existence of domains of univalence for the classes of holomorphic self-mappings of the disc with two fixed points and conditions on the values of angular derivatives at the boundary fixed points. The report is devoted to the development of these results. The sharp domains of univalence for classes of holomorphic self-mappings of the disc with repulsive boundary fixed point are found depending on the localization of the attracting fixed point and the value of the angular derivative at the repulsive fixed point.