Spectral synthesis in a complex domain for a differential operator with constant coefficients. II. The module method

The problem of spectral synthesis for a subspace $W$ invariant with respect to a differential operator with constant coefficients was reduced earlier to verification that its annihilator submodule $I=\operatorname{An}W$ is ample. In the present article the property of ampleness is split into two parts – stability, and the property of being saturated. The latter properties are subjected to a systematic investigation.