EAN: 9783030050191

NUMERICAL RANGE OF HOLOMORPHIC MAPPINGS AND APP...

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.

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