On the non-extendability of quasianalytic germs

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Let E₁(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,+∞[. We show that the ring E₁(M)+ contains elements that cannot be extended quasianalytically in a neighborhood of 0 in R, unless it coincides with the ring of real-analytic germs.