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arXiv · 1006.4171

On the non-extendability of quasianalytic germs

Vincent Thilliez
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Abstract

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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Vincent Thilliez. 2010-06-21. On the non-extendability of quasianalytic germs. https://arxiv.org/abs/1006.4171

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