Inverse Sturm-Liouville problem with analytical functions in the boundary condition

Natalia Bondarenko

doi:10.1002/mma.7375

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arXiv · 2002.12076

Inverse Sturm-Liouville problem with analytical functions in the boundary condition

Natalia Bondarenko

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Abstract

The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and develop a constructive algorithm for the inverse problem solution. The main results are applied to the Hochstadt-Lieberman half-inverse problem. As an auxiliary proposition, we prove local solvability and stability for the inverse Sturm-Liouville problem by the Cauchy data in the non-self-adjoint case.

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BibTeX RIS

Natalia Bondarenko. 2020-02-27. Inverse Sturm-Liouville problem with analytical functions in the boundary condition. https://doi.org/10.1002/mma.7375

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