Resumen de Caractérisation des anneaux noethériens de séries formelles à croissance controlée: application à la synthèse spectrale

Jacques Chaumat, Anne-Marie 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.