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010   $a3-030-05020-3
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100   $a20190311d2019      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aNumerical range of holomorphic mappings and applications /$fby Mark Elin, Simeon Reich, David Shoikhet
205   $a1st ed. 2019.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019.
215   $a1 online resource (238 pages)
311 08$a3-030-05019-X 
327   $aPreface -- 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.
330   $aThis 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. .
606   $aFunctional analysis
606   $aOperator theory
606   $aFunctions of complex variables
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139
606   $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074
615  0$aFunctional analysis.
615  0$aOperator theory.
615  0$aFunctions of complex variables.
615 14$aFunctional Analysis.
615 24$aOperator Theory.
615 24$aFunctions of a Complex Variable.
676   $a510
700   $aElin$b Mark$4aut$4http://id.loc.gov/vocabulary/relators/aut$0508326
702   $aReich$b Simeon$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aShoikhet$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910338260403321
996   $aNumerical Range of Holomorphic Mappings and Applications$92534323
997   $aUNINA