Converging semigroups of holomorphic maps

Marco Abate

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 2, page 223-227
  • ISSN: 1120-6330

Abstract

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In this paper we study the semigroups Φ : ℝ + → H ⁢ o ⁢ l ⁢ ( D , D ) of holomorphic maps of a strictly convex domain D ⊂ 𝐂 n into itself. In particular, we characterize the semigroups converging, uniformly on compact subsets, to a holomorphic map h : D → 𝐂 n .

How to cite

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Abate, Marco. "Converging semigroups of holomorphic maps." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.2 (1988): 223-227. <http://eudml.org/doc/287425>.

@article{Abate1988,
abstract = {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 $h : D \rightarrow \mathbf\{C\}^\{n\}$.},
author = {Abate, Marco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Semigroups of holomorphic maps; Convex domains; Iteration of holomorphic maps; Fixed points; iteration; semigroup; holomorphic maps},
language = {eng},
month = {6},
number = {2},
pages = {223-227},
publisher = {Accademia Nazionale dei Lincei},
title = {Converging semigroups of holomorphic maps},
url = {http://eudml.org/doc/287425},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Abate, Marco
TI - Converging semigroups of holomorphic maps
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/6//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 2
SP - 223
EP - 227
AB - 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 $h : D \rightarrow \mathbf{C}^{n}$.
LA - eng
KW - Semigroups of holomorphic maps; Convex domains; Iteration of holomorphic maps; Fixed points; iteration; semigroup; holomorphic maps
UR - http://eudml.org/doc/287425
ER -

References

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  1. ABATE, M.: Horospheres and iterates of holomorphic maps. «Math. Zeit.» 198 (1987) 225-238. Zbl0628.32035MR939538DOI10.1007/BF01163293
  2. ABATE, M.: Common fixed points of commuting holomorphic maps. «Math. Ann.» 283 (1989) 645-655. Zbl0646.32014MR990593DOI10.1007/BF01442858
  3. ABATE, M., VIGUÉ, J-P.: Coomon fixed points in hyperbolic Riemann surfaces and convex domains, Preprint, (1989). Zbl0724.32012MR1065938DOI10.2307/2048745
  4. BERKSON, E. and PORTA, H.: Semigroups of analytic functions and composition operators. «Mich. Math. J.» 25 (1978) 101-115. Zbl0382.47017MR480965
  5. DENJOY, A.: Sur l'itération des fonctions analytiques. «C.R. Acad. Sci. Paris» 182 (1926), 255-257. Zbl52.0309.04JFM52.0309.04
  6. KRANTZ, S.G.: Function theory of several complex variables. Wiley, New York, 1982. Zbl0471.32008MR635928
  7. NARASIMHAN, R.: Several complex variables. University of Chicago Press, Chicago, 1971. Zbl0223.32001MR342725
  8. VIGUÉ, J.P.: Points fixes d'applications holomorphes dans un domaine borné convexe de 𝐂 n . «Trans. Amer. Math. Soc.» 289 (1985), 345-353. Zbl0589.32043MR779068DOI10.2307/1999704
  9. 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. Zbl52.0309.02JFM52.0309.02
  10. WOLFF, J.: Sur l'itération des fonctions bornées. «C.R. Acad. Sci. Paris» 182 (1926), 200-201. Zbl52.0309.03JFM52.0309.03
  11. WOLFF, J.: Sur une généralisation d'un théorème de Schwarz. «C.R. Acad. Sci. Paris» 182 (1926), 918-920. Zbl52.0309.05JFM52.0309.05

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