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Simultaneous approximation by universal series. (English) Zbl 1194.41028

The author shows that, if individual universal series exist, then one can choose a sequence of universal series performing simultaneous universal approximation with the same sequence of indices. The existence of universal Laurent series on an annulus using only the existence of universal Taylor series on discs is derived as an application.

MSC:

41A28 Simultaneous approximation
30B30 Boundary behavior of power series in one complex variable; over-convergence
47A16 Cyclic vectors, hypercyclic and chaotic operators
30E10 Approximation in the complex plane
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