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Restricted Universality of Power Series
Author(s) -
Kahane JeanPierre,
Melas Antonios D.
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609301008384
Subject(s) - mathematics , radius of convergence , universality (dynamical systems) , power series , complement (music) , series (stratigraphy) , pure mathematics , convergence (economics) , radius , discrete mathematics , mathematical analysis , paleontology , biochemistry , chemistry , physics , computer security , quantum mechanics , complementation , biology , computer science , economics , gene , phenotype , economic growth
We prove the existence of a power series having radius of convergence 0, whose partial sums have universal approximation properties on any compact set with connected complement that is contained in a finite union of circles centred at 0 and having rational radii, but do not have such properties on any compact set with nonempty interior. This relates to a theorem of A. I. Seleznev. 2000 Mathematics Subject Classification 30B30 (primary), 30B10, 30E60 (secondary).