2024/06/04 by Mark Elin, Elin, Mark, Fiana Jacobzon +1
Engineering · Physics and Astronomy · #Complex Variables (math.CV) #Elasticity and Wave Propagation #FOS: Mathematics #Nonlinear Waves and Solitons #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.2406.02766
openalex publication_date 2024/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we present a unified approach to the study of geometric and dynamic properties of nonlinear resolvents of holomorphic generators. The idea is to apply the distortion theorem we have established. This method allows us to find order of spirallikeness and of strong starlikeness of resolvents and remove all the restrictions for resolvents to admit quasiconformal extension to the complex plane \C. In addition, we use this method to establish the uniform convergence of the resolvent family on the whole unit disk and obtain some characteristics of semigroups generated by these resolvents.