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.
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Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal, Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains. J. Eur. Math. Soc. 12 (2010), no. 1, pp. 23–53DOI 10.4171/JEMS/188