A generic result concerning univalent universal functions

Author： Costakis G.  

Publisher： Springer Publishing Company

ISSN： 0003-889X

Source： Archiv der Mathematik, Vol.82, Iss.4, 2004-04, pp. : 344-351

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Abstract

Let </mediaobject>$ \Omega $ be a Jordan region. We prove that generically every function </mediaobject>$ f \in H(\Omega) $ , univalent in </mediaobject>$ \Omega $ and continuous on </mediaobject>$ \overline\Omega $ is universal under derivatives and universal in respect to overconvergence. In fact f</i> realizes both approximations with the same approximative sequence. The proof is based on a modified version of the classical result of J. Walsh concerning approximation of holomorphic functions by polynomials.

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