TY - BOOK ID - 46189081 TI - Numerical range of holomorphic mappings and applications AU - Elin, Mark. AU - Reich, Simeon. AU - Shoikhet, David. PY - 2019 SN - 3030050203 303005019X PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Holomorphic mappings. KW - Mappings, Holomorphic KW - Functions of several complex variables KW - Mappings (Mathematics) KW - Functional analysis. KW - Operator theory. KW - Functions of complex variables. KW - Functional Analysis. KW - Operator Theory. KW - Functions of a Complex Variable. KW - Complex variables KW - Elliptic functions KW - Functions of real variables KW - Functional analysis KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations UR - https://www.unicat.be/uniCat?func=search&query=sysid:46189081 AB - 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. . ER -