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Théorèmes de préparation Gevrey et étude de certaines applications formelles

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Mouze A.

Annales Polonici Mathematici

2003

tom 81

nr 2

139-156

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.

Division dans l'anneau des séries formelles à croissance contrôlée. Applications

100%

Mouze A.

Studia Mathematica

2001

tom 144

nr 1

63-93

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 a Weierstrass-Hironaka division theorem for such subrings. Moreover, given an ideal ℐ of A and a series f in A we prove the existence in A of a unique remainder r modulo ℐ. As a consequence, we get a new proof of the noetherianity of A.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

2 Mouze A.

1 2003

1 2001

Wyniki wyszukiwania

Théorèmes de préparation Gevrey et étude de certaines applications formelles

Division dans l'anneau des séries formelles à croissance contrôlée. Applications