Abstract and Applied Analysis

Generation theory for semigroups of holomorphic mappings in Banach spaces

Simeon Reich and David Shoikhet

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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.

Article information

Abstr. Appl. Anal., Volume 1, Number 1 (1996), 1-44.

First available in Project Euclid: 7 April 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


Reich, Simeon; Shoikhet, David. Generation theory for semigroups of holomorphic mappings in Banach spaces. Abstr. Appl. Anal. 1 (1996), no. 1, 1--44. doi:10.1155/S1085337596000012. https://projecteuclid.org/euclid.aaa/1049725990

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