The paper studies short exact sequences of Banach modules over the convolution algebra L 1 = L 1 (G), where G is a compact abelian group. The main tool is the notion of a nonlinear centralizer, which in combination with the Fourier transform, is used to produce sequences of L 1 -modules 0 → Lq → Z → Lp → 0 that are nontrivial as long as the general theory allows it, namely forConcrete examples are worked in detail for the circle group, with applications to the Hardy classes, and the Cantor group.Résumé. -L'article étudie des suites exactes courtes de modules de Banach sur l'algèbre de convolution L 1 = L 1 (G), où G est un groupe abélien compact. L'outil principal est la notion de centralisateur non linéaire, qui, en combinaison avec la transformée de Fourier, est utilisée pour produire des suites exactes de L 1 -modules de la forme 0 → Lq → Z → Lp → 0 qui sont non triviales tant que la théorie générale le permet, à savoir pour p ∈ (1, ∞], q ∈ [1, ∞). Des exemples concrets sont détaillés pour le groupe du cercle, avec des applications aux classes de Hardy, et le groupe de Cantor.
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