Théorèmes de préparation Gevrey et étude de certaines applications formelles

Augustin Mouze

Annales Polonici Mathematici (2003)

  • Volume: 81, Issue: 2, page 139-156
  • ISSN: 0066-2216

Abstract

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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 be a formal power series. If F is a holomorphic map, the following result is well known: ∘ F is analytic implies there exists a convergent power series ˜ such that ∘ F = ˜ ∘ F . We get similar results when the map F is no longer holomorphic.

How to cite

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Augustin Mouze. "Théorèmes de préparation Gevrey et étude de certaines applications formelles." Annales Polonici Mathematici 81.2 (2003): 139-156. <http://eudml.org/doc/280814>.

@article{AugustinMouze2003,
author = {Augustin Mouze},
journal = {Annales Polonici Mathematici},
keywords = {formal power series; Gevrey series; preparation theorem; derivation},
language = {fre},
number = {2},
pages = {139-156},
title = {Théorèmes de préparation Gevrey et étude de certaines applications formelles},
url = {http://eudml.org/doc/280814},
volume = {81},
year = {2003},
}

TY - JOUR
AU - Augustin Mouze
TI - Théorèmes de préparation Gevrey et étude de certaines applications formelles
JO - Annales Polonici Mathematici
PY - 2003
VL - 81
IS - 2
SP - 139
EP - 156
LA - fre
KW - formal power series; Gevrey series; preparation theorem; derivation
UR - http://eudml.org/doc/280814
ER -

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