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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.

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

  • [1] T. H. MacGregor, Approximation by polynomials subordinate to a univalent function, Trans. Amer. Math. Soc. 148 (1970), 199-209. MR 41 #2029. MR 0257378 (41:2029)
  • [2] T. J. Suffridge, The principle of subordination applied to functions of several variables, Pacific J. Math. 33 (1970), 241-248. MR 41 #5660. MR 0261040 (41:5660)

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Keywords: Convex biholomorphic mappings, subordination of functions
Article copyright: © Copyright 1973 American Mathematical Society

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