On the non-extendability of quasianalytic germs

Details On the non-extendability of quasianalytic germs On the non-extendability of quasianalytic germs

2010-06-21

arxiv.org/abs/1006.4171v2

Mathematics

Classical Analysis and ODEs

This paper has been withdrawn since the author has found out that a similar result, with a slightly different proof, already a

Scientific paper

Let $\mathcal{E}_1(M)^+$ be the local ring of germs at 0 of functions
belonging to a given Denjoy-Carleman quasianalytic class in a neighborhood of 0
in $[0,+\infty[$. We show that the ring $\mathcal{E}_1(M)^+$ contains elements
that cannot be extended quasianalytically in a neighborhood of 0 in
$\mathbb{R}$, unless it coincides with the ring of real-analytic germs.

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