Solvability in gevrey classes of some linear functional equations

Abstract EN

In this paper, we associate to each number k > 0 a new class of linear endomorphisms of the sheaf of germs of holomorphic functions on [-1;1] and prove the solvability in the Gevrey class of some linear functional equations related to these endomorphisms.

We apply the result obtained to prove the solvability in the Gevrey class ?? ([-1;1]) of some linear functional equations