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Universal Taylor series. (English) Zbl 0865.30001
Summary: We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a \(G_\delta\)-dense subset of the space of holomorphic functions defined in the open unit disc. Our result provides the answer to a question stated by S. K. Pichorides concerning the limit set of Taylor series. Moreover, we study some properties of universal Taylor series and show, in particular, that they are trigonometric series in the sense of D. Menchoff.

30B50 Dirichlet series, exponential series and other series in one complex variable
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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