Uniform Stability of the Inverse Sturm-Liouville Problem with Polynomials in a Boundary Condition

This paper deals with the Sturm-Liouville problem with singular potential of the Sobolev space W2-1 and polynomials of the spectral parameter in a boundary condition. We prove the uniform boundedness and the uniform stability for the inverse spectral problem in the general non-self-adjoint case. It is remarkable that our stability estimates are valid for some cases with different degrees of the polynomials for two compared operators. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.