Physics

Pure mathematics

Mathematics

Mathematical physics

Mathematical analysis

Boundary value problem

Sturm–Liouville theory

Applied mathematics

Analysis and Mathematical Physics

We prove local solvability and stability for the inverse problem of recovering a complex-valued square integrable potential in the Sturm–Liouville equation on a finite interval from spectra of two boundary value problems with one common boundary condition. For this purpose we generalize classical Borg’s method to the case of multiple spectra.

On Borg’s method for non-selfadjoint Sturm–Liouville operators