On the Borel mapping in the quasianalytic setting

Abstract

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.

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

Cited by in corpus (10)

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• On generalized definitions of ultradifferentiable classes
• The Theorem of Iterates for elliptic and non-elliptic Operators
• The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spaces
• Ultradifferentiable extension theorems: a survey
• On the construction of large Algebras not contained in the image of the Borel map
• On the maximal extension in the mixed ultradifferentiable weight sequence setting
• The Borel map in the mixed Beurling setting
• On optimal solutions of the Borel problem in the Roumieu case
• How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes?