Spectral synthesis for systems of differential operators with constant coefficients (Q5934088)

Let \(G\subset\mathbb{C}\) be a convex domain, \(H\) the standard space of functions analytic on \(G\), \(\pi(z)= \{\pi_1(z),\dots, \pi_n(z)\}\) a fixed set of polynomials of one variable \(z\), and \(\pi(D)\) the corresponding system of differential operators. A closed subspace \(W\subset H\) is called \(\pi(D)\)-invariant if it is invariant under every operator of the system \(\pi(D)\). The problem of spectral synthesis for operators \(\pi(D)\) can be formulated as follows: find conditions under which the \(\pi(D)\) invariant substance \(W\subset H\) admits spectral synthesis. The paper gives some necessary and sufficient conditions, which generalize results of Krasichkov-Ternovskii when \(n= 1\).