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Universal Inner Functions on the Ball

  Published:2008-12-01
 Printed: Dec 2008
  • Frédéric Bayart
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Abstract

It is shown that given any sequence of automorphisms $(\phi_k)_k$ of the unit ball $\bn$ of $\cn$ such that $\|\phi_k(0)\|$ tends to $1$, there exists an inner function $I$ such that the family of ``non-Euclidean translates" $(I\circ\phi_k)_k$ is locally uniformly dense in the unit ball of $H^\infty(\bn)$.
Keywords: inner functions, automorphisms of the ball, universality inner functions, automorphisms of the ball, universality
MSC Classifications: 32A35, 30D50, 47B38 show english descriptions $H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]
Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
Operators on function spaces (general)
32A35 - $H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]
30D50 - Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
47B38 - Operators on function spaces (general)
 

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