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We characterize Gevrey functions on the unit interval [-1; 1] as sums of  holomorphic functions in specific neighborhoods of [-1; 1]. As an application  of our main theorem, we perform a simple proof for Dyn'kin's theorem of  pseudoanalytic extension for Gevrey classes on [-1; 1].

Développement en série de fonctions holomorphes des fonctions d'une classe de Gevrey sur l'intervalle [-1;1]