Théorèmes de préparation Gevrey et étude de certaines applications formelles

• Autorzy: Augustin Mouze
• Języki publikacji: FR EN

Abstrakty

EN

We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove preparation theorems of Malgrange type in these rings. As a consequence we study maps F from $ℂ^{s}$ to $ℂ^{p}$ without constant term such that the rank of the Jacobian matrix of F is equal to 1. Let 𝓐 be a formal power series. If F is a holomorphic map, the following result is well known: 𝓐 ∘ F is analytic implies there exists a convergent power series $\widetilde{𝓐}$ such that $𝓐 ∘ F= \widetilde{𝓐} ∘ F$. We get similar results when the map F is no longer holomorphic.

Kategorie tematyczne

• 13J05: Power series rings
• 13F25: Formal power series rings
• 14B12: Local deformation theory, Artin approximation, etc.
• 32B05: Analytic algebras and generalizations, preparation theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2003
• Tom: 81
• Numer: 2
• Strony: 139-156

Daty

wydano

2003

Twórcy

autor

Augustin Mouze

• Laboratoire de Mathématiques, UMR 8524, Université des Sciences et Technologies de Lille, 59650 Villeneuve d'Ascq Cedex, France

Identyfikatory

DOI

10.4064/ap81-2-5