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On a theorem of Seidel and Walsh

Authors:	Gerd Herzog

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

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

Keywords:	Primary 30H05
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