Locally explicit fundamental principle for homogeneous convolution equations

In the present paper a locally explicit version of Ehrenpreis's Fundamental Principle for a system of homogeneous convolution equations $\check{f}\ast \mu_j=0$, $j=1,\dots, m $, $f\in\mathcal{E}(\mathbb{R}^n)$, $\mu_j\in\mathcal{E}^{\prime}(\mathbb{R}^n)$, is derived, when the Fourier Transforms $\hat{\mu}_j$, $j=1,\dots, m$ are slowly decreasing entire functions that form a complete intersection in $\mathbb{C}^n$.