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Universal Singular Inner Functions

Published:2004-03-01
Printed: Mar 2004
• Pamela Gorkin
• Raymond Mortini
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Abstract

We show that there exists a singular inner function $S$ which is universal for noneuclidean translates; that is one for which the set $\{S(\frac{z+z_n}{1+\bar z_nz}):n\in\mathbb{N}\}$ is locally uniformly dense in the set of all zero-free holomorphic functions in $\mathbb{D}$ bounded by one.
 MSC Classifications: 30D50 - Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part