RECOVERING STURM–LIOUVILLE OPERATOR WITH TWO INTERIOR DISCONTINUITIES

In this paper, we study the Sturm–Liouville operator withtwo interior discontinuities and with spectral parameter linearly containedin one of the boundary conditions. Spectral properties of the eigenvaluesand norming constants of this operator are investigated. Moreover, theWeyl solution and the Weyl function for this operator are defined. Weprove uniqueness theorems for the solution of the inverse problems of reconstructionof the operator from the Weyl function, from the spectraldata and from two spectra. We give constructive procedures for solvingthese inverse problems.

Keywords:

Discontinuous Sturm–Liouville problems , eigenparameterdependent boundary conditions , jump conditions , Weyl function , inverse problem