Revistes Catalanes amb Accés Obert (RACO)

Caractérisation des anneaux noethériens de séries formelles à croissance controlée. Application à la synthèse spectrale

J. Chaumat, A.-M. Chollet


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.

Text complet: PDF (Français)