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.