Numerical Range of Holomorphic Mappings and Applications

Inbunden, Engelska, 2019

935 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2019-03-21
Mått:155 x 235 x 19 mm
Vikt:535 g
Format:Inbunden
Språk:Engelska
Antal sidor:229
Förlag:Springer Nature Switzerland AG
ISBN:9783030050191

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

“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)

Innehållsförteckning

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.