Some properties of (C,E,P)-algebras : Overgneration and 0-order estimates.

Antoine Delcroix (1, 2)

1 CRREF - Centre de recherches et de ressources en éducation et formation
2 AOC - Analyse Optimisation Controle

We give a new definition of the so-called overgenerated rings, which are the usual tool used to define the asymptotic structure of a (C,E,P)-algebra, written as a factor space M_{(A,E,P)}/N_{(I_{A},E,P)}. With this new definition and in the particular case of E=C^{∞}, we show that a moderate element i.e. in M_{(A,E,P)} is negligible if and only if it satisfies the C⁰-order estimate for the ideal N_{(I_{A},E,P)}.

Mots clés: Properties of non linear generalized functions; (C; P)-algebra

Domaines: Analyse fonctionnelle [math.FA]

Antoine Delcroix. Some properties of (C,E,P)-algebras : Overgneration and 0-order estimates.. 2008. ⟨hal-00326671⟩