On spectra of non-self-adjoint Sturm–Liouville operators

Abstract.

The spectra of non-self-adjoint Sturm-Liouville operators with distributional potentials belonging to the space W ⁻¹ ₂(0, 1) are studied. In particular, it is shown that any sequence of complex numbers obeying a specified asymptotics coincides with the spectrum of some non-self-adjoint Sturm-Liouville operator of the class under consideration. The inverse spectral problem of reconstructing an operator from two spectra or from one spectrum and suitably defined norming constants is also solved, and a complete description of the spectral data for the operators considered is given.