Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Commuting holomorphic functions
and hyperbolic automorphisms

Author: Chiara de Fabritiis
Journal: Proc. Amer. Math. Soc. 124 (1996), 3027-3037
MSC (1991): Primary 32A10; Secondary 30E25, 32A40, 32A30
MathSciNet review: 1371120
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a complete classification of the holomorphic self-maps of the unit ball of $\mathbf {C}^{n}$ into itself which commute with a given hyperbolic automorphism.

References [Enhancements On Off] (What's this?)

  • 1. M. Abate, Iteration theory of holomorphic mappings on taut manifolds, Mediterranean Press, Rende, 1989. MR 92i:32032
  • 2. M. Abate, J.-P. Vigué Common fixed points in hyperbolic Riemann surfaces and convex domains, Proc. Amer. Math. Soc. 112 (1991), 503--512. MR 91i:32027
  • 3. C.C. Cowen, Commuting analytic functions, Trans. Am. Math. Soc. 283 (1984), 685--695. MR 85i:30054
  • 4. C. de Fabritiis, G. Gentili, On holomorphic maps which commute with hyperbolic automorphisms, to appear in Advances in Math., 1995.
  • 5. T. Franzoni, E. Vesentini, Holomorphic maps and invariant distances, North-Holland, Amsterdam, 1980. MR 82a:32032
  • 6. M.H. Heins, A generalization of the Aumann-Carathéodory ``Starrheitssatz", Duke Math. J. 8 (1941), 312--316. MR 3:81a
  • 7. S. Krantz, Function theory of several complex variables, Wiley, New York, 1982. MR 84c:32001
  • 8. M. Kuczma, Functional equations in a single variable, PWN, Warzawa, 1968. MR 37:4441
  • 9. M. Kuczma, An introduction to the theory of functional equations and inequalities: Cauchy's equation and Jensen's inequality, PWN, Warzawa, 1985. MR 86i:39008
  • 10. W. Rudin, Function theory in the unit ball of ${ \mathbf C} ^{n}$, Springer, Berlin, 1980. MR 82i:32002
  • 11. A.L. Shields, On fixed points of commuting analytic functions, Proc. Amer. Math. Soc. 15 (1964), 703--706.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 32A10, 30E25, 32A40, 32A30

Retrieve articles in all journals with MSC (1991): 32A10, 30E25, 32A40, 32A30

Additional Information

Chiara de Fabritiis
Affiliation: International School for Advanced Studies, via Beirut 2-4, 34014, Trieste, Italy

Keywords: Commuting functions, hyperbolic automorphism, Wolff point
Received by editor(s): December 18, 1994
Communicated by: Eric Bedford
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society