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Universal Singular Inner Functions

Published online by Cambridge University Press:  20 November 2018

Pamela Gorkin
Affiliation:
Department of Mathematics Bucknell University Lewisburg, Pennsylvania 17837 USA, e-mail: pgorkin@bucknell.edu
Raymond Mortini
Affiliation:
Département de Mathématiques Université de Metz Ile du Saulcy F-57045 Metz France, e-mail: mortini@poncelet.univ-metz.fr
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Abstract

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We show that there exists a singular inner function $S$ which is universal for noneuclidean translates; that is one for which the set $\{S(\frac{z\,+\,{{z}_{n}}}{1\,+\,{{{\bar{z}}}_{n}}z})\,:\,n\,\in \,\mathbb{N}\}$ is locally uniformly dense in the set of all zero-free holomorphic functions in $\mathbb{D}$ bounded by one.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2004

References

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