  An original approach to the inverse scattering for Jacobi matrices was
suggested in a recent paper by Volberg-Yuditskii. The authors considered quite
sophisticated spectral sets (including Cantor sets of positive Lebesgue
measure), however they did not take into account the mass point spectrum. This
paper follows similar lines for the continuous setting with an absolutely
continuous spectrum on the half-axis and a pure point spectrum on the negative
half-axis satisfying the Blaschke condition. This leads us to the solution of
the inverse scattering problem for a class of canonical systems that
generalizes the case of Sturm-Liouville (Schr\"odinger) operator.
