On the absence of stability of bases in some Fréchet spaces
Date
2020-08
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Source Title
Analysis Mathematica
Print ISSN
0133-3852
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Springer Science and Business Media B.V.
Volume
46
Issue
4
Pages
761 - 768
Language
English
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Abstract
We show that, for each compact subset of the real line of infinite cardinality with an isolated point, the space of Whitney jets on the set does not possess a basis consisting only of polynomials. On the other hand, polynomials are dense in any Whitney space. Thus, there are no general results about stability of bases in Fréchet spaces.