An inverse problem by eigenvalues of four spectra (Q714089)

The author considers the inverse Sturm-Liouville problems defined on a finite interval and uses certain parts of the spectra of four boundary condition problems, namely the Dirichlet-Dirichlet, the Neumann-Dirichlet, the Dirichlet-Neumann and the Neumann-Neumann problem to recover the potential uniquely. The author gives conditions necessary and sufficient for four sequences of real numbers to be the squares of eigenvalues of certain parts of the spectra of the mentioned problems and describes the procedure of recovering the potential.