On the non-extendability of quasianalytic germs

الأصل · EN

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.