Characterization of Noetherian rings of formal power series with controlled growth. Application to spectral synthesis.

Jacques Chaumat; Anne-Marie Chollet

Publicacions Matemàtiques (1997)

  • Volume: 41, Issue: 2, page 545-561
  • ISSN: 0214-1493

Abstract

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Given a subring of the ring of formal power series defined by the growth of the coefficients, we prove a necessary and sufficient condition for it to be a noetherian ring. As a particular case, we show that the ring of Gevrey power series is a noetherian ring. Then, we get a spectral synthesis theorem for some classes of ultradifferentiable functions.

How to cite

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Chaumat, Jacques, and Chollet, Anne-Marie. "Caractérisation des anneaux noethériens de séries formelles à croissance controlée. Application à la synthèse spectrale.." Publicacions Matemàtiques 41.2 (1997): 545-561. <http://eudml.org/doc/41305>.

@article{Chaumat1997,
author = {Chaumat, Jacques, Chollet, Anne-Marie},
journal = {Publicacions Matemàtiques},
keywords = {Anillo local noetheriano; Series de potencias; Funciones diferenciables; Noetherian rings; spectral synthesis; ultradifferentiable classes; logarithmically convex sequence of positive numbers},
language = {fre},
number = {2},
pages = {545-561},
title = {Caractérisation des anneaux noethériens de séries formelles à croissance controlée. Application à la synthèse spectrale.},
url = {http://eudml.org/doc/41305},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Chaumat, Jacques
AU - Chollet, Anne-Marie
TI - Caractérisation des anneaux noethériens de séries formelles à croissance controlée. Application à la synthèse spectrale.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 2
SP - 545
EP - 561
LA - fre
KW - Anillo local noetheriano; Series de potencias; Funciones diferenciables; Noetherian rings; spectral synthesis; ultradifferentiable classes; logarithmically convex sequence of positive numbers
UR - http://eudml.org/doc/41305
ER -

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