Division by Flat Ultradifferentiable Functions and Sectorial Extensions
Abstract
We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at the vertex of $ S $ with a sharp rate of vanishing. This allows us to obtain a Borel-Ritt type theorem for $ \mathcal{A}_M(S) $ extending previous results by Schmets and Valdivia. We also derive a division property for ideals of flat ultradifferentiable functions, in the spirit of a classical $ C^\infty $ result of Tougeron.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- February 2006
- DOI:
- 10.48550/arXiv.math/0602366
- arXiv:
- arXiv:math/0602366
- Bibcode:
- 2006math......2366T
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- Mathematics - Complex Variables;
- 30E05;
- 30D60;
- 46E15;
- 26E10
- E-Print:
- Slight update of the published version. The definition of closedness in subsections 4.1 and 4.2 is less restrictive. One minor typo corrected