03374nam 22005295 450 991033826040332120251116212037.03-030-05020-310.1007/978-3-030-05020-7(CKB)4100000007761868(MiAaPQ)EBC5727956(DE-He213)978-3-030-05020-7(PPN)235234044(EXLCZ)99410000000776186820190311d2019 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNumerical range of holomorphic mappings and applications /by Mark Elin, Simeon Reich, David Shoikhet1st ed. 2019.Cham :Springer International Publishing :Imprint: Birkhäuser,2019.1 online resource (238 pages)3-030-05019-X 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.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. .Functional analysisOperator theoryFunctions of complex variablesFunctional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Functions of a Complex Variablehttps://scigraph.springernature.com/ontologies/product-market-codes/M12074Functional analysis.Operator theory.Functions of complex variables.Functional Analysis.Operator Theory.Functions of a Complex Variable.510Elin Markauthttp://id.loc.gov/vocabulary/relators/aut508326Reich Simeonauthttp://id.loc.gov/vocabulary/relators/autShoikhet Davidauthttp://id.loc.gov/vocabulary/relators/autBOOK9910338260403321Numerical Range of Holomorphic Mappings and Applications2534323UNINA