Spectral synthesis in a complex domain for a differential operator with constant coefficients. III: Ample submodules

In [1] and [2] the problem of spectral synthesis for a subspace $W$ invariant under a differential operator with constant coefficients was reduced to a check of two properties of its annihilator submodule $I=\operatorname{An}W$: stability and saturation. The present article describes a situation in which this check leads to a positive result, i.e., the annihilator submodule $I$ is ample.