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The Existence of Universal Inner Functions on the Unit Ball of $\mathbb{C}^n$ |
Canad. Math. Bull. 48(2005), 409-413
Published:2005-09-01
Printed: Sep 2005
Printed: Sep 2005
- P. M. Gauthier
- J. Xiao
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 |
| 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 part 47B38 - Operators on function spaces (general) |