English

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 00 of smooth functions to the sequence of iterated partial derivatives at 00. 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

R2 v1 2026-06-22T10:59:40.133Z