Generation theory for semigroups of holomorphic mappings in Banach spaces

We study nonlinear semigroups ofholomorphic mappings in Banach spaces and their infinitesimal generators. Using resolvents, we char- acterize, in particular, bounded holomorphic generators on bounded convex domains and obtain an analog ofthe Hille exponential f ormula. We then apply our results to the null point theory ofsemi-plus complete vector fields. We study the structure ofnull 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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