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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An approximation theorem for biholomorphic functions on $ D\sp{n}$


Author: Joseph A. Cima
Journal: Trans. Amer. Math. Soc. 175 (1973), 491-497
MSC: Primary 32E30
MathSciNet review: 0313547
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Abstract: Let F be a biholomorphic mapping of the polydisk $ {D^n}$ into $ {{\mathbf{C}}^n}$. We construct a sequence of polynomial mappings $ \{ {P_j}\} $ such that each $ {P_j}$ is subordinate to $ {P_{j + 1}}$, each $ {P_j}$ is subordinate to F and the $ {P_j}$ converge uniformly on compacta to F. The polynomials $ {P_j}$ are biholomorphic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0313547-1
PII: S 0002-9947(1973)0313547-1
Keywords: Convex biholomorphic mappings, subordination of functions
Article copyright: © Copyright 1973 American Mathematical Society