Multiply universal holomorphic functions

[摘要] Let O subset of C O not equal C, be an open set with simply connected components. In Theorem 1 we prove the existence of a holomorphic function phi on O, which has together with all its derivatives and all its antiderivatives six universal properties at the same time (based on the behaviour of sequences of derivatives or antiderivatives, overconvergence-phenomena, or properties of translates). In Theorem 2 we show that the family of all functions with these universal properties is a dense subset of the metric space H(O) of all holomorphic functions on O, if H(O) is endowed with the usual compact-open topology. (C) 1997 Academic Press.

[发布日期] 1997-05-01