On a representation of the solution of the inverse Sturm-Liouville problem on the entire line (Q897033)

The authors study the inverse scattering problem for the Sturm-Liouville equation on the entire line in the classical setting. They obtain sufficient conditions on the reflection coefficient, strenthening the result by \textit{B. M. Levitan} [Mat. Sb., Nov. Ser. 108(150), 350--357 (1979; Zbl 0407.34014)]. The authors also develop a functional-theoretic approach, which describes the solution of the inverse problem on the basis of the Markushevich problem for the Jost solutions. Representations of the Jost solutions are derived in terms of the solution of the corresponding singular integral equation.