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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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An approximation theorem for biholomorphic functions on $D^{n}$
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by Joseph A. Cima PDF
Trans. Amer. Math. Soc. 175 (1973), 491-497 Request permission

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
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 175 (1973), 491-497
  • MSC: Primary 32E30
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0313547-1
  • MathSciNet review: 0313547