Inverse scattering problems where the potential is not absolutely continuous on the known interior subinterval
arXiv:1712.07779 · doi:10.1063/1.5021268
Abstract
The inverse scattering problem for the Schrdinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely determined by the left (or right) reflection coefficient alone provided that the potential is known on a finite interval and it is not absolutely continuous on this known interval.