Year: 2021
Type: preprint
Abstract: We study nonlinear resolvents of holomorphic generators of one-parameter semigroups acting in the open unit disk. The class of nonlinear resolvents can be studied in the framework of geometric function theory because it consists of univalent functions. In this paper we establish distortion and covering results, find order of starlikeness and of strong starlikeness of resolvents. This provides that any resolvent admits quasiconformal extension to the complex plane $\C$. In addition, we obtain some characteristics of semigroups generated by these resolvents.
Source: arXiv (Cornell University)
Authors: Elin, Mark, Jacobzon, Fiana
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4288076073