Spectral synthesis for the differentiation operator on systems of curvilinear strips

Let $G_1,\dots,G_q$ be curvilinear strips in the complex plane, and $H(G_1),\dots,H(G_q)$ the spaces of holomorphic functions in the domains $G_1,\dots,G_q$, respectively, endowed with the usual topology of uniform convergence on compact sets. Denote the topological product $H=H(G_1)\times\dots\times H(G_q)$ by $H$. In this paper the structure of closed subspaces of $H$ that are invariant under the action of the operator of componentwise differentiation is investigated.