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

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.