Inverse Stieltjes-like Functions and Inverse Problems for Systems with Schrodinger Operator

A class of scalar inverse Stieltjes-like functions is realized as linear-fractional transformations of transfer functions of conservative systems based on a Schrodinger operator T-h in L-2 [a, + infinity) with a non-selfadjoint boundary condition. In particular it is shown that; any inverse Stieltjes function of this class can be realized in the unique way so that the main operator A possesses a special semi-boundedness property. We derive formulas that restore the system uniquely and allow to find the exact value of a non-real boundary parameter h of the operator T-h as well as a real parameter mu that appears in the construction of the elements of the realizing system. An elaborate investigation of these formulas shows the dynamics of the restored parameters h and mu in terms of the changing free term a from the integral representation of the realizable function.