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Universal Inner Functions on the Ball

Published online by Cambridge University Press:  20 November 2018

Frédéric Bayart
Frédéric Bayart*
Affiliation:
Laboratoire Bordelais d’Analyse et de Géométrie, UMR 5467, Université Bordeaux 1, 33405 Talence Cedex, France. e-mail: Frederic.Bayart@math.u-bordeaux1.fr
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Abstract

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It is shown that given any sequence of automorphisms ${{\left( {{\phi }_{k}} \right)}_{k}}$ of the unit ball ${{\mathbb{B}}_{N}}$ of ${{\mathbb{C}}^{N}}$ such that $\left\| {{\phi }_{k}}\left( 0 \right) \right\|$ tends to 1, there exists an inner function $I$ such that the family of “non-Euclidean translates” ${{\left( I\,\text{o}\,{{\phi }_{k}} \right)}_{k}}$ is locally uniformly dense in the unit ball of ${{H}^{\infty }}\left( {{\mathbb{B}}_{N}} \right)$ .

Keywords

32A3530D5047B38inner functionsautomorphisms of the balluniversality

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 4 , 01 December 2008, pp. 481 - 486
Copyright
Copyright © Canadian Mathematical Society 2008

References

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