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Author Elin, Mark,
Title Numerical range of holomorphic mappings and applications / Mark Elin, Simeon Reich, David Shoikhet.
Imprint Cham, Switzerland : Birkhauser, [2019]

View online
View online
Author Elin, Mark,
Subject Holomorphic mappings.
Alt Name Reich, Simeon,
Shoiykhet, David, 1953-
Description 1 online resource
polychrome rdacc
Contents Intro; Contents; Preface; Chapter 1 Semigroups of Linear Operators; 1.1 Linear operators. Spectrum and resolvent; 1.2 Continuous semigroups and their generators; 1.3 Numerical range of linear operators; 1.4 Analytic semigroups; 1.5 Cesaro and Abel averages of linear operators; 1.6 Abel averages: recent results; Chapter 2 Numerical Range; 2.1 Holomorphic mappings in Banach spaces; 2.2 Spectrum and resolvent of holomorphic mappings; 2.3 Numerical range; 2.4 Real part estimates; 2.5 Holomorphically dissipative and accretive mappings; 2.6 Growth estimates for the numerical range
2.7 Filtration of dissipative mappingsChapter 3 Fixed Points of Holomorphic Mappings; 3.1 Fixed points in the unit disk; 3.2 Fixed points in the Hilbert ball; 3.3 Boundary fixed points and the horosphere function; 3.4 Canonical representation of the fixed point set; 3.5 Around the Earle-Hamilton fixed point theorem; 3.6 Inexact orbits of holomorphic mappings; 3.7 The Bohl-Poincare-Krasnoselskii Theorem; 3.8 Fixed points of pseudo-contractive holomorphic mappings; Chapter 4 Semigroups of Holomorphic Mappings; 4.1 Generated semigroups; 4.2 Stationary points of semigroups
4.3 Flow invariance conditions4.4 Semi-complete vector fields on bounded symmetric domains; 4.5 Rates of convergence of semigroups; 4.6 Semigroups and pseudo-contractive holomorphic mappings; 4.7 Semigroups on the Hilbert ball; Chapter 5 Ergodic Theory of Holomorphic Mappings; 5.1 General remarks; 5.2 Power bounded holomorphic mappings; 5.3 Ergodicity and fixed points; 5.4 Numerical range and power boundedness; 5.5 Dissipative and pseudo-contractive mappings; 5.6 Examples; Chapter 6 Some Applications; 6.1 Bloch radii; 6.2 Radii of starlikeness and spirallikeness
6.3 Analytic extension of one-parameter semigroups6.4 Analytic extension of semigroups without stationary points; 6.5 Composition operators and semigroups; 6.6 Analytic semigroups of composition operators; 6.7 Semigroups of composition operators on Hp(II); Bibliography; Subject Index; Author Index
Bibliography Note Includes bibliographical references.
Summary This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L.A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.
Note Online resource; title from digital title page (viewed on May 07, 2019).
ISBN 9783030050207 (electronic book)
3030050203 (electronic book)
OCLC # 1090496591
Additional Format Print version: Elin, Mark. Numerical Range of Holomorphic Mappings and Applications. Cham : Birkhauser Verlag GmbH, 2019 9783030050191.

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