ORIGINAL ARTICLE
Uniform stability of the inverse problem for the non-self-adjoint Sturm–Liouville operator
Natalia P. Bondarenko,
Corresponding Author
Natalia P. Bondarenko
Department of Mechanics and Mathematics, Saratov State University, Saratov, Russia
S. M. Nikolskii Mathematical Institute, RUDN University, Moscow, Russia
Moscow Center of Fundamental and Applied Mathematics, Lomonosov Moscow State University, Moscow, Russia
Correspondence
Natalia P. Bondarenko, Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.
Email: [email protected]
Search for more papers by this authorNatalia P. Bondarenko,
Corresponding Author
Natalia P. Bondarenko
Department of Mechanics and Mathematics, Saratov State University, Saratov, Russia
S. M. Nikolskii Mathematical Institute, RUDN University, Moscow, Russia
Moscow Center of Fundamental and Applied Mathematics, Lomonosov Moscow State University, Moscow, Russia
Correspondence
Natalia P. Bondarenko, Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.
Email: [email protected]
Search for more papers by this authorFirst published: 17 July 2025
Abstract
In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm–Liouville problem that consists in the recovery of the potential and the parameters of the boundary conditions from the eigenvalues and the generalized weight numbers. The special case of simple eigenvalues, as well as the general case with multiple eigenvalues, is studied. We find various subsets in the space of spectral data, on which the inverse mapping is Lipschitz continuous, and obtain the corresponding unconditional uniform stability estimates. Furthermore, the conditional uniform stability of the inverse problem under a priori restrictions on the potential is studied. In addition, we prove the uniform stability of the inverse problem by the Cauchy data, which are convenient for numerical reconstruction of the potential and for applications to partial inverse problems.
CONFLICT OF INTEREST STATEMENT
The authors declare no conflicts of interest.
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