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.
@article{urn:eudml:doc:41305,
title = {Caract\'erisation des anneaux noeth\'eriens de s\'eries formelles \`a croissance control\'ee. Application \`a la synth\`ese spectrale.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {545-561},
mrnumber = {MR1485503},
zbl = {0906.46017},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41305}
}
Chaumat, Jacques; Chollet, Anne-Marie. Caractérisation des anneaux noethériens de séries formelles à croissance controlée. Application à la synthèse spectrale.. Publicacions Matemàtiques, Tome 41 (1997) pp. 545-561. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41305/