Result: Analytic continuation of functions from invariant subspaces in convex domains of the complex space

Let \(D\) and \(G\), \(D\subset G\) be convex domains in \(\mathbb{C}^n\) and let \(W\) be an invariant subspace of \(H(D)\), the space of the holomorphic functions in \(D\), in the sense that if \(f\) belongs to \(W\) then its partial derivatives also belong to it. The paper deals with the question of the analytical continuation of the functions from \(D\) to \(G\). Several strong theorems are proved that improve the known previous results.