Local solvability and stability of the inverse problem for the non-self-adjoint Sturm–Liouville operator

Abstract

Abstract We consider the non-self-adjoint Sturm–Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local solvability and stability of this inverse problem, relying on the method of spectral mappings. Possible splitting of multiple eigenvalues is taken into account.

Keywords

• Inverse spectral problems
• Non-self-adjoint Sturm–Liouville operator
• Generalized spectral data
• Local solvability
• Stability
• Method of spectral mappings