Inverse Sturm-Liouville problem with analytical functions in the boundary condition
Spectral Theory
2021-09-01 v1
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.
Cite
@article{arxiv.2002.12076,
title = {Inverse Sturm-Liouville problem with analytical functions in the boundary condition},
author = {Natalia Bondarenko},
journal= {arXiv preprint arXiv:2002.12076},
year = {2021}
}