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Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces als Buch
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Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces

Sprache: Englisch.
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Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov … weiterlesen
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Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces als Buch

Produktdetails

Titel: Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces
Autor/en: Simeon Reich, David Shoikhet

ISBN: 1860945759
EAN: 9781860945755
Sprache: Englisch.
IMPERIAL COLLEGE PR

Juli 2005 - gebunden - 354 Seiten

Beschreibung

Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces. Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments.

Inhaltsverzeichnis

# Mappings in Metric and Normed Spaces # Differentiable and Holomorphic Mappings in Banach Spaces # Hyperbolic Metrics on Domains in Complex Banach Spaces # Some Fixed Point Principles # The Denjoy-Wolff Fixed Point Theory # Generation Theory for One-Parameter Semigroups # Flow-Invariance Conditions # Stationary Points of Continuous Semigroups # Asymptotic Behavior of Continuous Flows # Geometry of Domains in Banach Spaces

Pressestimmen

"The authors have done a very good job of collecting material scattered in the literature, and have been very precise in attributing results to the original authors. The book also contains an impressive number of examples and references." Mathematical Reviews "The present book provides a comprehensive, self-contained introduction to the modern theory of one-parameter semigroups, their stationary points and limiting behaviour. The reviewer strongly recommends the book to researchers who would like to become familiar with the area. The book is well-written and the material nicely presented. This book could also provide, either in total or in part, the basis of a graduate course in the theory of iterations and/or semigroups of holomorphic mappings." Zentralblatt MATH
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