Abstract and Applied Analysis
Volume 1 (1996), Issue 1, Pages 1-44

Generation theory for semigroups of holomorphic mappings in Banach spaces

Simeon Reich1 and David Shoikhet2

1Department of Mathematics, The Technion - Israel Institute of Technology, Haifa 32000, Israel
2Department of Applied Mathematics, International College of Technology, Karmiel 20101, Israel

Received 20 September 1995

Copyright © 1996 Simeon Reich and David Shoikhet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.