| Description |
1 online resource (xii, 264 pages) : figure |
| Series |
Operator theory, advances and applications ; v. 208 |
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Linear operators & linear systems |
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Operator theory, advances and applications ; v. 208.
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Operator theory, advances and applications. Linear operators and linear systems.
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| Contents |
Cover -- Table of Contents -- Preface -- Chapter 1 Geometric Background -- 1.1 Some classes of univalent functions -- 1.1.1 Starlike functions -- 1.1.2 Class S8727;[0]. Nevanlinnas condition -- 1.1.3 Classes S8727;[964;], 964; 8712; 916;. Hummels representation -- 1.1.4 Spirallike functions. 25;Spa25;ceks condition -- 1.1.5 Close-to-convex and 981;-like functions -- 1.2 Boundary behavior of holomorphic functions -- 1.3 The Julia8211;Wolff8211;Carath180;eodory and Denjoy8211;Wolff Theorems -- 1.4 Functions of positive real part -- Chapter 2 Dynamic Approach -- 2.1 Semigroups and generators -- 2.2 Flow invariance conditions and parametric representations of semigroup generators -- 2.3 The Denjoy8211;Wolff and Julia8211;Wolff8211;Carath180;eodory Theorems for semigroups -- 2.4 Generators with boundary null points -- 2.5 Univalent functions and semi-complete vector fields -- Chapter 3 Starlike Functions with Respect to a Boundary Point -- 3.1 Robertsons classes. Robertsons conjecture -- 3.2 Auxiliary lemmas -- 3.3 A generalization of Robertsons conjecture -- 3.4 Angle distortion theorems -- 3.4.1 Smallest exterior wedge -- 3.4.2 Biggest interior wedge -- 3.5 Functions convex in one direction -- Chapter 4 Spirallike Functions with Respect to a Boundary Point -- 4.1 Spirallike domains with respect to a boundary point -- 4.2 A characterization of spirallike functions with respect to a boundary point -- 4.3 Subordination criteria for the class Spiral956;[1] -- 4.4 Distortion Theorems -- 4.4.1 8216;Spiral angle distortion theorems -- 4.4.2 Growth estimates for semigroup generators -- 4.4.3 Growth estimates for spirallike functions -- 4.4.4 Classes G(956;, 946;) -- 4.5 Covering theorems for starlike and spirallike functions -- Chapter 5 Koenigs Type Starlike and Spirallike Functions -- 5.1 Schr168;oders and Abels equations -- 5.2 Remarks on stochastic branching processes -- 5.3 Koenigs linearization model for dilation type semigroups. Embeddings -- 5.4 Valirons type linearization models for hyperbolic type semigroups. Embeddings -- 5.5 Pommerenkes and Baker8211;Pommerenkes linearization models for semigroups with a boundary sink point -- 5.5.1 Pommerenkes linearization model for automorphic type mappings -- 5.5.2 Baker8211;Pommerenkes model for non-automorphic type self-mappings -- 5.5.3 Higher order angular differentiability at boundary fixed points. A unified model -- 5.6 Embedding property via Abels equation -- Chapter 6 Rigidity of Holomorphic Mappings and Commuting Semigroups -- 6.1 The Burns8211;Krantz theorem -- 6.2 Rigidity of semigroup generators -- 6.3 Commuting semigroups of holomorphic mappings -- 6.3.1 Identity principles for commuting semigroups -- 6.3.2 Dilation type -- 6.3.3 Hyperbolic type -- 6.3.4 Parabolic type -- Chapter 7 Asymptotic Behavior of One-parameter Semigroups -- 7.1 Dilation case -- 7.1.1 General remarks and rates of convergence -- 7.1.2 Argument rigidity principle -- 7.2 Hyperbolic case -- 7.2.1 Criteria for the exponential convergence -- 7.2.2 Angular similarity principle -- 7.3 Parabolic case -- 7.3.1 Discrete case -- 7.3.2 Continuous case -- 7.3.3 Universal asymptotes -- Chapter 8 Backward Flow Invariant Domains for Semigroups -- 8.1 Existence -- 8.2 Maximal FIDs. Flower structures -- 8.3 |
| Summary |
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, Schroder'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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Differentiable dynamical systems.
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Linear models (Statistics)
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Univalent functions.
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Functional equations.
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Semigroups.
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MATHEMATICS -- Differential Equations -- General.
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Ecuaciones funcionales
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Sistemas dinámicos diferenciables
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Differentiable dynamical systems
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Functional equations
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Linear models (Statistics)
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Semigroups
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Univalent functions
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Dynamisches System
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Komplexe Funktion
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Schlichte Funktion
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Funktionalgleichung
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Halbgruppe
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| Form |
Electronic book
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| ISBN |
9783034605090 |
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3034605099 |
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