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Numerical range of holomorphic mappi...

Elin, Mark.

Numerical range of holomorphic mappings and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical range of holomorphic mappings and applicationsby Mark Elin, Simeon Reich, David Shoikhet.
Author:	Elin, Mark.
other author:	Reich, Simeon.
Published:	Cham :Springer International Publishing :2019.
Description:	xiv, 229 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Holomorphic mappings.
Online resource:	https://doi.org/10.1007/978-3-030-05020-7
ISBN:	9783030050207$q(electronic bk.)

Numerical range of holomorphic mappings and applications
Elin, Mark.

Numerical range of holomorphic mappings and applications[electronic resource] /by Mark Elin, Simeon Reich, David Shoikhet. - Cham :Springer International Publishing :2019. - xiv, 229 p. :ill., digital ;24 cm.

Preface -- Semigroups of Linear Operators -- Numerical Range -- Fixed Points of Holomorphic Mappings -- Semigroups of Holomorphic Mappings -- Ergodic Theory of Holomorphic Mappings -- Some Applications -- Bibliography -- Subject Index -- Author Index.

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.

ISBN: 9783030050207$q(electronic bk.)

Standard No.: 10.1007/978-3-030-05020-7doiSubjects--Topical Terms:

247447
Holomorphic mappings.

LC Class. No.: QA331

Dewey Class. No.: 515.9

Numerical range of holomorphic mappings and applications
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100 1 $a Elin, Mark. $3 497814
245 1 0 $a Numerical range of holomorphic mappings and applications $h [electronic resource] / $c by Mark Elin, Simeon Reich, David Shoikhet.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a xiv, 229 p. : $b ill., digital ; $c 24 cm.
505 0 $a Preface -- Semigroups of Linear Operators -- Numerical Range -- Fixed Points of Holomorphic Mappings -- Semigroups of Holomorphic Mappings -- Ergodic Theory of Holomorphic Mappings -- Some Applications -- Bibliography -- Subject Index -- Author Index.
520 $a 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.
650 0 $a Holomorphic mappings. $3 247447
650 1 4 $a Functional Analysis. $3 274845
650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Functions of a Complex Variable. $3 275780
700 1 $a Reich, Simeon. $3 677378
700 1 $a Shoikhet, David. $3 497815
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-05020-7
950 $a Mathematics and Statistics (Springer-11649)