
Numerical Range of Holomorphic Mappings and Applications
Birkhäuser (Publisher)
Published on 21. March 2019
Book
Hardback
XIV, 229 pages
978-3-030-05019-1 (ISBN)
Description
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.
Reviews / Votes
"The book will serve as an excellent resource for mathematicians and applied scientists working at the frontier of the field and/or in the range of its applications. The book can also serve as an excellent graduate text for young and aspiring researchers in the field of infinite-dimensional holomorphy." (Abebaw Tadesse, Mathematical Reviews, December, 2019)More details
Product info
Book
Edition
2019
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
Bibliographie
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 19 mm
Weight
535 gr
ISBN-13
978-3-030-05019-1 (9783030050191)
DOI
10.1007/978-3-030-05020-7
Schweitzer Classification
Other editions
Additional editions

Mark Elin | Simeon Reich | David Shoikhet
Numerical Range of Holomorphic Mappings and Applications
E-Book
03/2019
1st Edition
Birkhäuser
€90.94
Available for download
Content
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.