An approximation theorem for biholomorphic functions on $D^{n}$
HTML articles powered by AMS MathViewer
- 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.References
- Thomas H. MacGregor, Approximation by polynomials subordinate to a univalent function, Trans. Amer. Math. Soc. 148 (1970), 199–209. MR 257378, DOI 10.1090/S0002-9947-1970-0257378-7
- T. J. Suffridge, The principle of subordination applied to functions of several variables, Pacific J. Math. 33 (1970), 241–248. MR 261040
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