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On a theorem of Seidel and Walsh

Authors:	Gerd Herzog

Institution:	(1) Mathematisches Institut I, Universität Karlsruhe, Postfach 6980, 76128 Karlsruhe, Germany

Abstract:	Given a sequence (_n) _n in $\mathbb{D}$ with $\mathop {\lim }\limits_{n \to \infty } \|\alpha _n \| = 1$ there are functions $f \in H(\mathbb{D})$ such that $\{ f \circ S_{\alpha _n } :n \in \mathbb{N}\} ,S_{\alpha _n } (z) = (z - \alpha _n )/(1 - \tilde \alpha _n z)$ , is a dense subset of $H(\mathbb{D})$ , and the set of functions with this property is residual in $H(\mathbb{D})$ . We will show that in $A(\mathbb{D})$ and some related Banach spaceX there are functionsf with $\{ f' \circ S_{\alpha _n } :n \in \mathbb{N}\}$ is dense in $H(\mathbb{D})$ , and we will give a sufficient condition when the set of such functions is residual inX.

Keywords:	Primary 30H05
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