Inverse Spectral Problem for Differential Operators With Rational Scattering Matrix Functions, Journal of Differential Equations
In this paper we obtain explicit formulas for the potential of an ordinary differential operator if its spectral function or its scattering functions are rational matrix functions which are analytic and invertible on the real line including infinity. The solution is given in terms of a realization of the spectral function or of the scattering function.
D. Alpay and I. Gohberg, Inverse spectral problem for differential operators with rational scattering matrix functions, Journal of differential equations, vol. 118 (1995) 1-19.