Completion problems and scattering problems for Dirac type differential   equations with singularities
  A completion problem to recover a rational matrix function which is j-unitary on the line is treated. A Dirac type system with singularities on the semiaxis is recovered explicitly by its left reflection coefficient. The close connection between these two problems is discussed. 
Bernd Fritzsche, Bernd Kirstein, and Alexander Sakhnovich