Universal functions as series of rational functions

We show that universal Taylor series in unbounded non-simply connected domains can be represented as series of rational functions with a double simultaneous approximation property. The use of Baire’s category theorem allows us to obtain strong results. Moreover, we extend our results from the holomo...

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Bibliographic Details
Published inRevista matemática complutense Vol. 27; no. 1; pp. 225 - 239
Main Authors Lamprecht, Martin, Nestoridis, Vassili
Format Journal Article
LanguageEnglish
Published Milan Springer Milan 2014
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Topology
Baire’s category theorem
Rational function
Universal function
Chordal metric
30K05
Uniform approximation
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Summary:We show that universal Taylor series in unbounded non-simply connected domains can be represented as series of rational functions with a double simultaneous approximation property. The use of Baire’s category theorem allows us to obtain strong results. Moreover, we extend our results from the holomorphic case to the meromorphic one, where we use the chordal metric.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-013-0116-4