# Solvability in Gevrey classes of some linear functional equations

## TL;DR

This paper introduces a new class of endomorphisms for holomorphic functions and proves the solvability of certain linear functional equations within Gevrey classes, advancing understanding of functional equation solutions in complex analysis.

## Contribution

It establishes the solvability of linear functional equations in Gevrey classes using a novel class of endomorphisms associated with positive numbers.

## Key findings

- Solvability of linear functional equations in Gevrey classes G_k([-1,1])
- Introduction of a new class of endomorphisms for holomorphic functions
- Extension of functional equation theory in complex analysis

## Abstract

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