Mixed data in inverse spectral problems for the Schrödinger operators

We consider the Schrödinger operator on a finite interval with an $L^1$-potential. prove that potential can be uniquely recovered from one spectrum and subsets of another point masses spectral measure (or norming constants) corresponding to first spectrum. also solve this Borg–Marchenko-type problem under some conditions two spectra, when missing part second known have different index sets.