Journal of the European Mathematical Society


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

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) Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica, 00133, ROMA, ITALY
(2) Departamento de Matemática Aplicada II, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092, SEVILLA, SPAIN
(3) Departamento de Matemática Aplicada II, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092, 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 F, Contreras M, Díaz-Madrigal S. 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