Sur les idéaux d'une algèbre de Beurling généralisée

Abstract

In this paper, we characterize the closed ideals of locally m-convex algebras as the linear closed subspaces that are invariant under translation. We also give a weighted algebra analogues of the classical theorems of N. Wiener and P. Lé́ vy on absolutely convergent Fourier series.

Keywords

• Algèbre localement m-convexe commutative, produit de convolution, poids sur R^n , transformation de Fourier, idéal d’une algèbre, théorème de Lévi, théorème tauberien de Wiener