# Solving An Inverse Problem For The Sturm-Liouville Operator With A Singular Potential By Yurko's Method

## DOI:

https://doi.org/10.5556/j.tkjm.52.2021.3700## Keywords:

inverse spectral problems; Sturm-Liouville operator; singular potential; method of spectral mappings## Abstract

An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution and obtain necessary and sufficient conditions of solvability for the inverse problem in the self-adjoint and the non-self-adjoint cases.

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*Tamkang Journal of Mathematics*,

*52*(1), 125-154. https://doi.org/10.5556/j.tkjm.52.2021.3700

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