For which classes of systems of linear second-order hyperbolic PDEs $Lf=g$ in $n$ variables are spaces $S$ of smooth (i.e., $C^\infty$) functions known with the following property (R):

(R) For every $g\in S$, there is a unique retarded solution of $Lf=g$ that is again in $S$?

Where can I read about the mathematical trools for this and similar questions?