Uniform stability for the inverse Sturm-Liouville problem with eigenparameter-dependent boundary conditions

Abstract: We consider a class of self-adjoint Sturm-Liouville problems with rational functions of the spectral parameter in the boundary conditions. The uniform stability for direct and inverse spectral problems is proved for the first time for Sturm-Liouville operator pencils with boundary conditions depending on the eigenparameter. Furthermore, we obtain stability estimates for finite data approximations, which are important from the practical viewpoint. Our method is based on Darboux-type transforms and proving of their Lipschitz continuity.