Inverse spectral problems for Sturm–Liouville operators with singular potentials. Part III: Reconstruction by three spectra

Abstract

We solve the inverse spectral problem of recovering the singular potential from W −1 2(0,1) of a Sturm–Liouville operator by its spectra on the three intervals [0,1], [0, a], and [ a,1] for some a∈(0,1). Necessary and sufficient conditions on the spectral data are derived, and uniqueness of the solution is analyzed.