ENGLISH

Semigroups in Geometrical Function Theory

By D. Shoikhet

Book information

Publisher
Springer
Year
2001
ISBN
0792371119, 9780792371113
LCC
QA360 .S58 2001
Open Library ID
OL19697822M
Language
english
Format
PDF
Filesize
3 MB (2776517 bytes)
Edition
1
Pages
233\233
DPI
600
Orientation
yes
Scanned
yes
Time added
2012-02-04 16:00:00

Description

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 Poincar? 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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