ON THE INVERSE PROBLEM OF A DISSIPATIVE SCATTERING-THEORY .3.

Considering a scattering theory in the class of contractions on HILBERT spaces the inverse problem is solved in an operator-theoretical manner. The solution is obtained under the very general assumptions that the free evolutions are different for different time directions and that not only the perturbed or full evolutions but also the free evolutions are given by contractions. It is shown that the class of contractive HANKEL operators can be viewed as a set of scattering operators. This implies the possibility that the scattering operator can be compact. Moreover, the result is applied to the so-called LAX-PHILLIPS scattering theory with losses restoring a result of B. S. PAVLOV on the completion of this theory in a quite different manner.