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

An inverse problem for the Sturm-Liouville pencil with arbitrary entire functions in the boundary condition

“…For a real-valued potential q(x) and h ∈ R, Proposition 4.7 is the classical result by Borg (see [17, Theorem 1.8.1]). In the complex case, the similar proposition has been recently proved by Buterin and Kuznetsova (see [11]) for the Dirichlet boundary condition y(0) = 0 at the left. The case of the Robin boundary condition (1.2) has no principal differences.…”

“…We work with the complex-valued potential q(x) and possibly multiple eigenvalues. To deal with the inverse problem, having eigenparameter independent boundary conditions, we apply the Borg-type theorem, recently proved in [11] for the complex-valued potential.…”

Solvability and stability of the inverse Sturm–Liouville problem with analytical functions in the boundary condition

“…The conditions (ii) and (iii) are trivial corollaries of the asymptotic formula . The condition (iv) also follows from Equation (see the proof in Buterin and Kuznetsova, Appendix). Thus, ( C 1 ) is proved.…”

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

“…Some fragmentary results on stability under splitting of multiple eigenvalues were obtained in [17][18][19] for various inverse problems. Recently Buterin and Kuznetsova [20] proved local solvability and stability for the inverse problem by two spectra for the nonself-adjoint Sturm-Liouville operator. They also took splitting of multiple eigenvalues into account.…”