On the Borel mapping in the quasianalytic setting
Classical Analysis and ODEs
2017-10-24 v3 Functional Analysis
Abstract
The Borel mapping takes germs at of smooth functions to the sequence of iterated partial derivatives at . 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.
Cite
@article{arxiv.1509.05565,
title = {On the Borel mapping in the quasianalytic setting},
author = {Armin Rainer and Gerhard Schindl},
journal= {arXiv preprint arXiv:1509.05565},
year = {2017}
}
Comments
14 pages; minor changes, accepted for publication in Math. Scand.; typos corrected and numbering of equations changed in order to be in accordance with the published article