Converging semigroups of holomorphic maps

Abate, Marco

Abate, Marco

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 82 (1988), p. 223-227 / Harvested from Biblioteca Digitale Italiana di Matematica

Access to full text
Full (PDF)
Full (DjVu)

Abstract
Résumé

In this paper we study the semigroups $\Phi:\mathbb{R}^{+}\rightarrow Hol(D,D)$ of holomorphic maps of a strictly convex domain $D\subset\mathbf{C}^{n}$ into itself. In particular, we characterize the semigroups converging, uniformly on compact subsets, to a holomorphic map $h:D\rightarrow\mathbf{C}^{n}$ .

In questa nota vengono caratterizzati quei semigruppi $\Phi:\mathbb{R}^{+}\rightarrow Hol(D,D)$ di applicazioni olomorfe di un dominio strettamente convesso $D\subset\mathbf{C}^{n}$ in sé che convergono, uniformemente sui compatti, ad un'applicazione olomorfa $h:D\rightarrow\mathbf{C}^{n}$ .

Publié le : 1988-06-01

MR 1152644 | Zbl 0723.32012

@article{RLINA_1988_8_82_2_223_0,
     author = {Marco Abate},
     title = {Converging semigroups of holomorphic maps},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {82},
     year = {1988},
     pages = {223-227},
     zbl = {0723.32012},
     mrnumber = {1152644},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1988_8_82_2_223_0}
}

Abate, Marco. Converging semigroups of holomorphic maps. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 82 (1988) pp. 223-227. http://gdmltest.u-ga.fr/item/RLINA_1988_8_82_2_223_0/

Bibliographie

[1] Abate, M.: Horospheres and iterates of holomorphic maps. «Math. Zeit.» 198 (1987) 225-238. | MR 939538 | Zbl 0628.32035

[2] Abate, M.: Common fixed points of commuting holomorphic maps. «Math. Ann.» 283 (1989) 645-655. | MR 990593 | Zbl 0646.32014

[2a] Abate, M., Vigué, J-P.: Coomon fixed points in hyperbolic Riemann surfaces and convex domains, Preprint, (1989). | MR 1065938 | Zbl 0724.32012

[3] Berkson, E. and Porta, H.: Semigroups of analytic functions and composition operators. «Mich. Math. J.» 25 (1978) 101-115. | MR 480965 | Zbl 0382.47017

[4] Denjoy, A.: Sur l'itération des fonctions analytiques. «C.R. Acad. Sci. Paris» 182 (1926), 255-257. | JFM 52.0309.04

[5] Krantz, S.G.: Function theory of several complex variables. Wiley, New York, 1982. | MR 635928 | Zbl 0471.32008

[6] Narasimhan, R.: Several complex variables. University of Chicago Press, Chicago, 1971. | MR 342725 | Zbl 0223.32001

[7] Vigué, J.P.: Points fixes d'applications holomorphes dans un domaine borné convexe de $\mathbf{C}^{n}$ . «Trans. Amer. Math. Soc.» 289 (1985), 345-353. | MR 779068 | Zbl 0589.32043

[8] Wolff, J.: Sur l'itération des fonctions holomorphes dans une région, et dont les valeurs appartiennent à cette région. «C.R. Acad. Sci. Paris» 182 (1926), 42-43. | JFM 52.0309.02

[9] Wolff, J.: Sur l'itération des fonctions bornées. «C.R. Acad. Sci. Paris» 182 (1926), 200-201. | JFM 52.0309.03

[10] Wolff, J.: Sur une généralisation d'un théorème de Schwarz. «C.R. Acad. Sci. Paris» 182 (1926), 918-920. | JFM 52.0309.05