Recovering Sturm-Liouville operators with a discontinuous weight function

In this study, we investigate the inverse problem for Sturm-Liouville differential operators on a finite interval having a discontinuous weight function. We give properties of the spectral characteristics and prove the uniqueness theorem for the inverse problem of recovering operators.

Keywords:

Inverse problem , Sturm-Liouville equation , Piece-wise continuous function , Weyl function