Geodesic
Universal Inner Functions on the Ball
Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 481-486

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DOI

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 ${{H}^{\infty }}\left( {{\mathbb{B}}_{N}} \right)$ .
DOI : 10.4153/CMB-2008-048-8
Mots-clés : 32A35, 30D50, 47B38, inner functions, automorphisms of the ball, universality 
Bayart, Frédéric. Universal Inner Functions on the Ball. Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 481-486. doi: 10.4153/CMB-2008-048-8
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     title = {Universal {Inner} {Functions} on the {Ball}},
     journal = {Canadian mathematical bulletin},
     pages = {481--486},
     year = {2008},
     volume = {51},
     number = {4},
     doi = {10.4153/CMB-2008-048-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-048-8/}
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