Let D be a hyperbolic convex domain in a complex Banach space. Let the mapping F ∈ Hol(D,D) be bounded on each subset strictly inside D, and have a nonempty fixed point set ℱ in D. We consider several methods for constructing retractions onto ℱ under local assumptions of ergodic type. Furthermore, we study the asymptotic behavior of the Cesàro averages of one-parameter semigroups generated by holomorphic mappings.
@article{bwmeta1.element.bwnjournal-article-smv130i3p231bwm,
author = {Simeon Reich and David Shoikhet},
title = {Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {231-244},
zbl = {0918.46046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv130i3p231bwm}
}
Reich, Simeon; Shoikhet, David. Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains. Studia Mathematica, Tome 129 (1998) pp. 231-244. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv130i3p231bwm/
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