Generation theory for semigroups of holomorphic mappings in Banach spaces
Reich, Simeon ; Shoikhet, David
Abstr. Appl. Anal., Tome 1 (1996) no. 1, p. 1-44 / Harvested from Project Euclid
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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.
Publié le : 1996-05-14
Classification:  Banach space,  Cauchy problem,  exponential formula,  holomorphic generator,  hyperbolic metric,  Lie generator,  nonlinear semigroup,  null point,  resolvent,  spectrum,  32H15,  34G20,  46G20,  47H10,  47H15,  47H20 
@article{1049725990,
     author = {Reich, Simeon and Shoikhet, David},
     title = {Generation theory for semigroups of holomorphic mappings
in Banach spaces},
     journal = {Abstr. Appl. Anal.},
     volume = {1},
     number = {1},
     year = {1996},
     pages = { 1-44},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1049725990}
}

Reich, Simeon; Shoikhet, David. Generation theory for semigroups of holomorphic mappings
in Banach spaces. Abstr. Appl. Anal., Tome 1 (1996) no. 1, pp.  1-44. http://gdmltest.u-ga.fr/item/1049725990/