Elin / Reich / Shoikhet Numerical Range of Holomorphic Mappings and Applications

1. Auflage 2019
ISBN: 978-3-030-05020-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 229 Seiten, eBook

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.

Zielgruppe

Research

Autoren/Hrsg.

Elin, Mark

Reich, Simeon

Shoikhet, David

Inhaltsverzeichnis

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.