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# The Existence of Universal Inner Functions on the Unit Ball of $\mathbb{C}^n$

Published:2005-09-01
Printed: Sep 2005
• P. M. Gauthier
• J. Xiao
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## Abstract

It is shown that there exists an inner function $I$ defined on the unit ball ${\bf B}^n$ of ${\mathbb C}^n$ such that each function holomorphic on ${\bf B}^n$ and bounded by $1$ can be approximated by non-Euclidean translates" of $I$.
 Keywords: universal inner functions universal inner functions
 MSC Classifications: 32A35 - $H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15] 30D50 - Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part47B38 - Operators on function spaces (general)