The interlacing of spectra between continuous and discontinuous sturm-liouville problems and its application to inverse problems

The discontinuous Sturm-Liouville problem defined on [0, 1] with jump conditions at point d ∈ (0, 1) is considered. The interlacing of the spectra between the discontinuous Sturm-Liouville problem and two Sturm-Liouville problems defined on [0, d] and [d, 1] is provided. As the application of this interlacing to inverse problems, we prove that the potential is determined uniquely by the three spectra generated by the discontinuous Sturm-Liouville problem and two Sturm-Liouville problems defined on [0, d] and [d, 1].