Synthesis in the Polynomial Kernel of Two Analytic Functionals

Let $\pi $ be an entire function of minimal type and order $\rho=1$ and let $\pi (D)$ be the corresponding differential operator. Maximal $\pi (D)$-invariant subspace of the kernel of an analytic functional is called its $\mathbf{C}[\pi ]$-kernel. $\mathbf{C}[\pi ]$-kernel of a system of analytic functionals is called the intersection of their $\mathbf{C}[\pi ]$-kernels. The paper describes the conditions which allow synthesis of $\mathbf{C}[\pi ]$-kernels of two analytical functionals with respect to the root elements of the differential operator $\pi (D)$.