Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
In rings $Γ_{M}$ of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence $M = (M_{l})_{l≥0}$ (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in $Γ_{M}$ such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to $Γ_{M}$, provided $Γ_{M}$ is stable under derivation. By a further development of the method, we obtain the main result of the paper, stating that the ideals generated by a given analytic germ in rings of ultradifferentiable germs are closed provided the generator is homogeneous and has an isolated singularity in ℝⁿ. The result is valid under the aforementioned assumption of stability under derivation, and it does not involve (non-)quasianalyticity properties.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
49-65
Opis fizyczny
Daty
wydano
2002
Twórcy
autor
- CNRS-UMR 8524, Bâtiment M2, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-1-4