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

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.  2003 Elsevier Inc. All rights reserved