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Compositional universality in the N-dimensional ball
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L. Bernal-González
Published/Copyright:
September 25, 2009
It is proved in this note that a sequence of automorphisms on the N-dimensional unit ball acts properly discontinuously if and only if its corresponding sequence of composition operators is universal on the Hardy space of such ball, and if and only if there exists a dense linear manifold of universal functions. Our result completes earlier ones by several authors.
Keywords: Hardy space; Seidel–Walsh theorem; composition operator; N-dimensional ball; algebraically generic universality
Received: 2005-11-29
Published Online: 2009-9-25
Published in Print: 2006-9-1
© Oldenbourg Wissenschaftsverlag
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Keywords for this article
Hardy space;
Seidel–Walsh theorem;
composition operator;
N-dimensional ball;
algebraically generic universality
Articles in the same Issue
- Universal overconvergence of homogeneous expansions of harmonic functions
- Joint universality for sums and products of Dirichlet L-functions
- On the speed of convergence to limit distributions for Hecke L-functions associated with ideal class characters
- Universal Taylor series on unbounded open sets
- Universality for generalized Euler products
- Universal Taylor series on non-simply connected domains
- Compositional universality in the N-dimensional ball
- A discrete universality theorem for general Dirichlet series
- On the zeros of T-universal functions
- A Liouville-type result for lacunary power series and converse results for universal holomorphic functions
- Universal Taylor series on open subsets of Rn
- A universal harmonic function which is bounded on each line
- The joint universality for periodic Hurwitz zeta-functions
