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

Elmostafa Bendib, Hicham Zoubeir

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 $[-1,1]$.