Sectorial Stieltjes functions and their realizations by L-systems with a Schrodinger operator

We consider classes of sectorial Stieltjes functions. It is shown that a function belonging to these classes can be realized as the impedance function of a singular L-system with a sectorial state-space operator. We provide an additional condition on a given function from this class so that the state-space operator of the realizing L-system is a-sectorial with the exact angle of sectoriality a. Then these results are applied to L-systems based upon a non-self-adjoint Schrodinger operator.