Division by Flat Ultradifferentiable Functions and Sectorial Extensions
| dc.creator | Thilliez, Vincent | |
| dc.date | 2006-02-17 | |
| dc.date.accessioned | 2026-07-07T07:03:31Z | |
| dc.date.available | 2026-07-07T07:03:31Z | |
| dc.description | 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. | |
| dc.description | Slight update of the published version. The definition of closedness in subsections 4.1 and 4.2 is less restrictive. One minor typo corrected | |
| dc.identifier | https://arxiv.org/abs/math/0602366 | |
| dc.identifier | http://arxiv.org/abs/math/0602366 | |
| dc.identifier | Results in Mathematics 44 (2003), 169-188 | |
| dc.identifier | doi:10.1007/s00025-003-0081-1 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109003 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 30E05; 30D60; 46E15; 26E10 | |
| dc.title | Division by Flat Ultradifferentiable Functions and Sectorial Extensions | |
| dc.type | text |