Semigroups in Geometrical Function Theory

Name: Semigroups in Geometrical Function Theory
Brand: Springer Netherlands
SKU: 9780792371113
Price: 59.36 EUR
Availability: InStock

Автор: D. Shoikhet

Език:

Корици: С твърди корици

Издател: Springer Netherlands

Наличност: Външен склад в ограничено количество

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59.36 € 116.09 лв

This manuscript provides an introduction to the generation theory of nonlinear one-parameter semigro...

Информация за книгата

Автор

D. Shoikhet

Език

Английски език

Корици

Книга - С твърди корици

Издадена

2001

страници

222

EAN

9780792371113

ISBN

0792371119

Enbook ID

01396862

Издател

Springer Netherlands

Теглоt

549

Размери

167 x 240 x 15

Пълно описание

This manuscript provides an introduction to the generation theory of nonlinear one-parameter semigroups on a domain of the complex plane in the spirit of the Wolff-Denjoy and Hille-Yoshida theories. Special attention is given to evolution equations reproduced by holomorphic vector fields on the unit disk. A dynamic approach to the study of geometrical properties of univalent functions is emphasized. The book comprises six chapters. The preliminary chapter and chapter 1 give expositions to the theory of functions in the complex plane, and the iteration theory of holomorphic mappings according to Wolff and Denjoy, as well as to Julia and Caratheodory. Chapter 2 deals with elementary hyperbolic geometry on the unit disk, and fixed points of those mappings which are nonexpansive with respect to the Poincaré metric. Chapters 3 and 4 study local and global characteristics of holomorphic and hyperbolically monotone vector-fields, which yield a global description of asymptotic behavior of generated flows. Various boundary and interior flow invariance conditions for such vector-fields and their parametric representations are presented. Applications to univalent starlike and spirallike functions on the unit disk are given in Chapter 5. The approach described may also be useful for higher dimensions. Audience: The book will be of interest to graduate students and research specialists working in the fields of geometrical function theory, iteration theory, fixed point theory, semigroup theory, theory of composition operators and complex dynamical systems.

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Semigroups in Geometrical Function Theory

Информация за книгата

Пълно описание

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