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Analysis and Mathematical Physics

, Volume 9, Issue 4, pp 2133–2150 | Cite as

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

  • Sergey ButerinEmail author
  • Maria Kuznetsova
Article
  • 49 Downloads

Abstract

We prove local solvability and stability for the inverse problem of recovering a complex-valued square integrable potential in the Sturm–Liouville equation on a finite interval from spectra of two boundary value problems with one common boundary condition. For this purpose we generalize classical Borg’s method to the case of multiple spectra.

Keywords

Inverse spectral problem Non-selfadjoint Sturm–Liouville operator Borg’s method Nonlinear integral equation Stability 

Mathematics Subject Classification

34A55 34B24 47E05 

Notes

Acknowledgements

This work was supported in part by the Ministry of Education and Science of Russian Federation (Grant 1.1660.2017/4.6) and by the Russian Foundation for Basic Research (Grant 19-01-00102).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.

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© Springer Nature Switzerland AG 2019
corrected publication 2019

Authors and Affiliations

  1. 1.Department of MathematicsSaratov State UniversitySaratovRussia

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