Assumption: Flat Green package

The componentwise retarded and advanced Green operators $G_{\mathrm{R}},G_{\mathrm{A}}$ act on compact tensor distributions and satisfy:

1. $$\square G_{\mathrm{R}}a=a=\square G_{\mathrm{A}}a,G_{\mathrm{R}}\square a=a=G_{\mathrm{A}}\square a(a\in {{\mathcal{D}}^{\prime }}_c);$$
2. $$\mathrm{supp}(G_{\mathrm{R}}a)\subseteq J^{+}(\mathrm{supp}a),\mathrm{supp}(G_{\mathrm{A}}a)\subseteq J^{-}(\mathrm{supp}a);$$

3. they commute with constant-coefficient differential operators and with $T$;

4. they take compact smooth sources to smooth solutions;

5. the corresponding retarded, advanced, and smooth Cauchy uniqueness statements hold.