On the Borel mapping in the quasianalytic setting - Rainer, Armin; Schindl, Gerhard (MATHEMATICA SCANDINAVICA, 2017)
The Borel mapping takes germs at $0$ of smooth functions to the sequence of iterated partial derivatives at $0$. We prove that the Borel mapping restricted to the germs of any quasianalytic ultradifferentiable class strictly larger than the real analytic class is never onto the corresponding sequence space.