Caractérisation des anneaux noethériens de séries formelles à croissance controlée. Application à la synthèse spectrale.
Jacques Chaumat, Anne-Marie Chollet (1997)
Publicacions Matemàtiques
Similarity:
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.