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
DOI:
https://doi.org/10.1090/S0002-9939-96-03729-X
MathSciNet review:
1371120
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Abstract | References | Similar Articles | Additional Information
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.
- 1. Marco Abate, Iteration theory of holomorphic maps on taut manifolds, Research and Lecture Notes in Mathematics. Complex Analysis and Geometry, Mediterranean Press, Rende, 1989. MR 1098711
- 2. Marco Abate and Jean-Pierre Vigué, Common fixed points in hyperbolic Riemann surfaces and convex domains, Proc. Amer. Math. Soc. 112 (1991), no. 2, 503–512. MR 1065938, https://doi.org/10.1090/S0002-9939-1991-1065938-8
- 3. Carl C. Cowen, Commuting analytic functions, Trans. Amer. Math. Soc. 283 (1984), no. 2, 685–695. MR 737892, https://doi.org/10.1090/S0002-9947-1984-0737892-8
- 4. C. de Fabritiis, G. Gentili, On holomorphic maps which commute with hyperbolic automorphisms, to appear in Advances in Math., 1995.
- 5. Tullio Franzoni and Edoardo Vesentini, Holomorphic maps and invariant distances, Notas de Matemática [Mathematical Notes], vol. 69, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 563329
- 6. M.H. Heins, A generalization of the Aumann-Carathéodory ``Starrheitssatz", Duke Math. J. 8 (1941), 312--316. MR 3:81a
- 7. Steven G. Krantz, Function theory of several complex variables, John Wiley & Sons, Inc., New York, 1982. Pure and Applied Mathematics; A Wiley-Interscience Publication. MR 635928
- 8. Marek Kuczma, Functional equations in a single variable, Monografie Matematyczne, Tom 46, Państwowe Wydawnictwo Naukowe, Warsaw, 1968. MR 0228862
- 9. Marek Kuczma, An introduction to the theory of functional equations and inequalities, Prace Naukowe Uniwersytetu Śląskiego w Katowicach [Scientific Publications of the University of Silesia], vol. 489, Uniwersytet Śląski, Katowice; Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1985. Cauchy’s equation and Jensen’s inequality; With a Polish summary. MR 788497
- 10. Walter Rudin, Function theory in the unit ball of 𝐶ⁿ, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
- 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:
https://doi.org/10.1090/S0002-9939-96-03729-X
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