Extended abstract theory of universal series and applications

In this article, we extend the recently developed abstract theory of universal series to include averaged sums of the form for a given fixed sequence of vectors ( x j ) in a topological vector space X over a field of real or complex scalars, where is a sequence of non-zero field scalars. We give nec...

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Bibliographic Details
Published in:Monatshefte für Mathematik 2009-10, Vol.158 (2), p.151-178
Main Author: Hadjiloucas, Demetris
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In this article, we extend the recently developed abstract theory of universal series to include averaged sums of the form for a given fixed sequence of vectors ( x j ) in a topological vector space X over a field of real or complex scalars, where is a sequence of non-zero field scalars. We give necessary and sufficient conditions for the existence of a sequence of coefficients ( a j ) which make the above sequence of averaged sums dense in X . When applied, the extended theory gives new analogues to well known classical theorems including those of Seleznev, Fekete and Menchoff.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-008-0038-2