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Semigroups in Geometrical Function Theory - D. Shoikhet
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D. Shoikhet:
Semigroups in Geometrical Function Theory - pocketboek

ISBN: 9048157471

[SR: 9177970], Paperback, [EAN: 9789048157471], Springer, Springer, Book, [PU: Springer], Springer, Historically, complex analysis and geometrical function theory have been inten­ sively developed from the beginning of the twentieth century. They provide the foundations for broad areas of mathematics. In the last fifty years the theory of holomorphic mappings on complex spaces has been studied by many mathemati­ cians with many applications to nonlinear analysis, functional analysis, differential equations, classical and quantum mechanics. The laws of dynamics are usually presented as equations of motion which are written in the abstract form of a dy­ namical system: dx / dt + f ( x) = 0, where x is a variable describing the state of the system under study, and f is a vector function of x. The study of such systems when f is a monotone or an accretive (generally nonlinear) operator on the under­ lying space has been recently the subject of much research by analysts working on quite a variety of interesting topics, including boundary value problems, integral equations and evolution problems (see, for example, [19, 13] and [29]). In a parallel development (and even earlier) the generation theory of one­ parameter semigroups of holomorphic mappings in en has been the topic of interest in the theory of Markov stochastic processes and, in particular, in the theory of branching processes (see, for example, [63, 127, 48] and [69])., 13911, Differential Equations, 226699, Applied, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 13930, Analytic Geometry, 226700, Geometry & Topology, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 13955, Mathematical Analysis, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 13905, Calculus, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 13920, Functional Analysis, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 13940, Group Theory, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books

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ISBN: 9789048157471

ID: 978904815747

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. D. Shoikhet, Books, Science and Nature, Semigroups in Geometrical Function Theory Books>Science and Nature, Springer Netherlands

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Semigroups in Geometrical Function Theory als Buch von D. Shoikhet - D. Shoikhet
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Semigroups in Geometrical Function Theory als Buch von D. Shoikhet - gebonden uitgave, pocketboek

2001, ISBN: 9789048157471

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Semigroups in Geometrical Function Theory:Softcover reprint of hardcover 1st ed. 2001. D. Shoikhet Semigroups in Geometrical Function Theory:Softcover reprint of hardcover 1st ed. 2001. D. Shoikhet Bücher > Wissenschaft > Mathematik, Springer

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Semigroups in Geometrical Function Theory - D. Shoikhet
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D. Shoikhet:
Semigroups in Geometrical Function Theory - pocketboek

ISBN: 9789048157471

ID: 9789048157471

Mathematics; Functions of a Complex Variable; Difference and Functional Equations; Geometry; Convex and Discrete Geometry; Special Functions Dimension, Grad, dynamical systems Books Book (Paperback Initiative), Springer Science+Business Media

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Semigroups in Geometrical Function Theory - D. Shoikhet
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Semigroups in Geometrical Function Theory - pocketboek

ISBN: 9789048157471

ID: 9789048157471

Semigroups in Geometrical Function Theory Semigroups-in-Geometrical-Function-Theory~~D-Shoikhet Science>Mathematics>Mathematics Paperback, Springer Netherlands

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Semigroups in Geometrical Function Theory

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.

Gedetalleerde informatie over het boek. - Semigroups in Geometrical Function Theory


EAN (ISBN-13): 9789048157471
ISBN (ISBN-10): 9048157471
Gebonden uitgave
pocket book
Verschijningsjaar: 2010
Uitgever: Springer-Verlag GmbH
236 Bladzijden
Gewicht: 0,363 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 16.02.2011 13:59:45
Boek voor het laatst gevonden op 02.01.2018 19:22:21
ISBN/EAN: 9789048157471

ISBN - alternatieve schrijfwijzen:
90-481-5747-1, 978-90-481-5747-1


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