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Restricted Universality of Power Series |
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| Authors: | Kahane, Jean-Pierre Melas, Antonios D. |
| Affiliation: | Batiment 425 (Mathematique), Université de Paris-Sud 91405 Orsay Cedex, France; jean-pierre.kahane{at}math.u-psud.fr Department of Mathematics, University of Athens Panepistimiopolis, Athens 157-84, Greece; amelas{at}math.uoa.gr |
| Abstract: | We prove the existence of a power series having radius of convergence0, whose partial sums have universal approximation propertieson any compact set with connected complement that is containedin a finite union of circles centred at 0 and having rationalradii, but do not have such properties on any compact set withnonempty interior. This relates to a theorem of A. I. Seleznev.2000 Mathematics Subject Classification 30B30 (primary), 30B10,30E60 (secondary). |
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