Journal of the European Mathematical Society


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Volume 12, Issue 1, 2010, pp. 23–53
DOI: 10.4171/JEMS/188

Published online: 2009-12-23

Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains

Filippo Bracci[1], Manuel D. Contreras[2] and Santiago Díaz-Madrigal[3]

(1) Università di Roma 'Tor Vergata', Italy
(2) Universidad de Sevilla, Spain
(3) Universidad de Sevilla, Spain

We characterize infinitesimal generators of semigroups of holomorphic self-maps of strongly convex domains using the pluricomplex Green function and the pluricomplex Poisson kernel. Moreover, we study boundary regular fixed points of semigroups. Among other things, we characterize boundary regular fixed points both in terms of the boundary behavior of infinitesimal generators and in terms of pluripotential theory.

Keywords: Semigroups, boundary fixed points, infinitesimal generators, iteration theory, pluripotential theory

Bracci Filippo, Contreras Manuel, Díaz-Madrigal Santiago: Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains. J. Eur. Math. Soc. 12 (2010), 23-53. doi: 10.4171/JEMS/188