Inverse spectral problems for energy-dependent Sturm-Liouville equations

摘要

We study the inverse spectral problem of reconstructing energy-dependentSturm-Liouville equations from their Dirichlet spectra and sequences of thenorming constants. For the class of problems under consideration, we give acomplete description of the corresponding spectral data, suggest areconstruction algorithm, and establish uniqueness of reconstruction. Theapproach is based on connection between spectral problems for energy-dependentSturm-Liouville equations and for Dirac operators of special form.