Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces.
This book focuses on a systematic survey and detailed treatment of linearization models for one-parameter semigroups, Schröder’s and Abel’s functional equations, and various classes of univalent functions which serve as intertwining mappings for nonlinear and linear semigroups. These topics are applicable to the study of problems in complex analysis, stochastic and evolution processes and approximation theory.
Spis treści
Geometric Background.- Dynamic Approach.- Starlike Functions with Respect to a Boundary Point.- Spirallike Functions with Respect to a Boundary Point.- Kœnigs Type Starlike and Spirallike Functions.- Rigidity of Holomorphic Mappings and Commuting Semigroups.- Asymptotic Behavior of One-parameter Semigroups.- Backward Flow Invariant Domains for Semigroups.- Appendices.
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