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].

In this note we obtain a new convergence result for the Adomian decomposition method.2010 Mathematics Subject Classification.. 97N40.

This modest work is dedicated to the memory of our beloved master Ahmed Intissar , a distinguished professor,a brilliant mathematician,a man with a golden heart.Abstract. In this paper we consider the difference equation (E) :are given real constants, a j (j = 1, ..., q) are given holomorphic functions on some strip R δ (δ > 0) such that a 1 and aq are nowhere vanishing on R δ , and χ a function which belongs to a quasianalytic Carleman class C M {R}. We prove under a growth condition on the functions a j that the equation (E) is solvable in the class C M {R}.2010 Mathematics Subject Classification.. 30H05; 30B10; 30D05.

This modest work is dedicated to the memory of our beloved master Ahmed Intissar , a brilliant mathematician (PhD at M.I.T, Cambridge), a distinguished professor, a man with a golden heart.