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Commuting holomorphic functions and hyperbolic automorphisms
Author(s):
Chiara
de Fabritiis
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3027-3037.
MSC (1991):
Primary 32A10;
Secondary 30E25, 32A40, 32A30
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Abstract:
We give a complete classification of the holomorphic self-maps of the unit ball of  into itself which commute with a given hyperbolic automorphism.
References:
- 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
 , 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.
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Additional Information:
Chiara
de Fabritiis
Affiliation:
International School for Advanced Studies, via Beirut 2-4, 34014, Trieste, Italy
Email:
FABRITII@NEUMANN.SISSA.IT
DOI:
10.1090/S0002-9939-96-03729-X
PII:
S 0002-9939(96)03729-X
Keywords:
Commuting functions,
hyperbolic automorphism,
Wolff point
Received by editor(s):
December 18, 1994
Communicated by:
Eric Bedford
Copyright of article:
Copyright
1996,
American Mathematical Society
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