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The Existence of Universal Inner Functions on the Unit Ball of ℂn

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier  and
J. Xiao
P. M. Gauthier
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, Montréal, QC, H3C 3J7 e-mail: gauthier@dms.umontreal.ca
J. Xiao
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7 e-mail: jxiao@math.mun.ca
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Abstract

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It is shown that there exists an inner function $I$ defined on the unit ball ${{\text{B}}^{n}}$ of ${{\mathbb{C}}^{n}}$ such that each function holomorphic on ${{\text{B}}^{n}}$ and bounded by 1 can be approximated by “non-Euclidean translates” of $I$.

Keywords

32A3530D5047B38universal inner functions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 3 , 01 September 2005 , pp. 409 - 413
Copyright
Copyright © Canadian Mathematical Society 2005

References

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