On the non-extendability of quasianalytic germs

Vincent Thilliez

On the non-extendability of quasianalytic germs

Classical Analysis and ODEs 2010-09-08 v2 Functional Analysis

Authors: Vincent Thilliez

Abstract

Let $\mathcal{E}_1(M)^+$ be the local ring of germs at 0 of functions belonging to a given Denjoy-Carleman quasianalytic class in a neighborhood of 0 in $[0,+\infty[$ . We show that the ring $\mathcal{E}_1(M)^+$ contains elements that cannot be extended quasianalytically in a neighborhood of 0 in $\mathbb{R}$ , unless it coincides with the ring of real-analytic germs.

Keywords

quasianalytic germs Denjoy-Carleman class non-extendability local ring real-analytic germs

Cite

@article{arxiv.1006.4171,
  title  = {On the non-extendability of quasianalytic germs},
  author = {Vincent Thilliez},
  journal= {arXiv preprint arXiv:1006.4171},
  year   = {2010}
}

Comments

This paper has been withdrawn since the author has found out that a similar result, with a slightly different proof, already appeared in a paper of M. Langenbruch (Manuscripta Math. 83 (1994), 123-143; see the remark after Corollary 2.4)

On the non-extendability of quasianalytic germs

Abstract

Keywords

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