This book examines 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.

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.

Important step towards establishing a bridge between nonlinear semigroup theory, functional and differential equations and geometric function theory Self-contained presentation with a complete account of definitions, proofs and references Presentation of relevant prerequisites from iteration theory, fixed point theory and univalent functions Includes supplementary material: sn.pub/extras

Klappentext
This book provides valuable insights into complex analysis, dynamical systems, geometric function theory and operator theory. Intended for a broad spectrum of readers, ranging from undergraduate and graduate mathematics students to active researchers, it offers extensive coverage of recent advances in geometric function theory, including the theory of starlike and spirallike functions with respect to a boundary point. Of particular interest is its treatment of continuous time semigroups, about which little has been previously known, emphasizing the use of generation theory for continuous dynamical systems. Such semigroups have important applications in such areas as composition operators, Markov stochastic processes, control theory and optimization. Readers will find in this book a systematic and detailed survey of linearization models for one-parameter continuous semigroups, functional equations, and the different classes of univalent functions which serve as intertwining mappings for these semigroups, along with their applications to various problems of complex dynamics.

Inhalt
Geometric Background.- Dynamic Approach.- Starlike Functions with Respect to a Boundary Point.- Spirallike Functions with Respect to a Boundary Point.- Knigs 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.