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1996 Generation theory for semigroups of holomorphic mappings in Banach spaces
Simeon Reich, David Shoikhet
Abstr. Appl. Anal. 1(1): 1-44 (1996). DOI: 10.1155/S1085337596000012


We study nonlinear semigroups of holomorphic mappings in Banach spaces and their infinitesimal generators. Using resolvents, we characterize, in particular, bounded holomorphic generators on bounded convex domains and obtain an analog of the Hille exponential formula. We then apply our results to the null point theory of semi-plus complete vector fields. We study the structure of null point sets and the spectral characteristics of null points, as well as their existence and uniqueness. A global version of the implicit function theorem and a discussion of some open problems are also included.


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Simeon Reich. David Shoikhet. "Generation theory for semigroups of holomorphic mappings in Banach spaces." Abstr. Appl. Anal. 1 (1) 1 - 44, 1996.


Published: 1996
First available in Project Euclid: 7 April 2003

zbMATH: 0945.46026
MathSciNet: MR1390558
Digital Object Identifier: 10.1155/S1085337596000012

Primary: 32H15 , 34G20
Secondary: 46G20 , 47H10 , 47H15 , 47H20

Keywords: Banach space , Cauchy problem , exponential formula , holomorphic generator , hyperbolic metric , Lie generator , nonlinear semigroup , null point , resolvent , spectrum

Rights: Copyright © 1996 Hindawi


Vol.1 • No. 1 • 1996
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