Abstract
Given a sequence (α 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.
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Herzog, G. On a theorem of Seidel and Walsh. Period Math Hung 30, 205–210 (1995). https://doi.org/10.1007/BF01876619
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DOI: https://doi.org/10.1007/BF01876619