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Some remarks on abstract universal series. (English) Zbl 1266.30050

Summary: We introduce a new class of Universal series, in the abstract setting. This class lies between two already known classes of Universal series. By two examples we differentiate these classes. These examples are the first examples in the case where all classes are non-void. We also prove that the class of Universal series where the approximating indexes have upper density 1 is dense and \(G_\delta \) and that the class of lower frequently universal series is of the first category.

MSC:

30K05 Universal Taylor series in one complex variable
30Kxx Universal holomorphic functions of one complex variable
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