Abstract
We give a description of those functions f in the unit ball 
of H
∞ on the disk \(\mathbb{D}\) whose orbit {f∘ϕ
n
: n∈ℕ} is locally uniformly dense in 
for some sequence (ϕ
n
) of selfmaps of \(\mathbb{D}\). An interpretation of this result in terms of the superposition (or substitution) operator on the space 
of holomorphic selfmaps of \(\mathbb{D}\) is given, too. Finally we present a new class of functions in H
∞ whose orbit in H
2 under the hyperbolic composition operator is non-minimal.
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Mortini, R. Superposition operators, 
-universal functions, and the hyperbolic composition operator.
Acta Math Hung 138, 267–280 (2013). https://doi.org/10.1007/s10474-012-0251-2
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DOI: https://doi.org/10.1007/s10474-012-0251-2
Key words and phrases
-
-universal function - cyclic vector
- Hardy–Hilbert space
- interpolating Blaschke product
- selfmap of the disk
- maximal ideal space
- Gleason part
-universal function