Inverse problem for Sturm-Liouville operators with Coulomb potential which have discontinuity conditions inside an interval
The authors examine the inverse spectral problem related to the singular Sturm-Liouville problem defined by \[ -y^{\prime \prime }(x)+\frac{c}{x}y(x)+q(x)y(x), \] where \(x\in (0,\pi ]\) and boundary conditions \(y(0)=y(\pi )=0\) and a jump condition \[ y(d+0)=\alpha y(d-0)\quad\text{ and }\quad y^{\prime }(d+0)=1/\alpha y^{\prime }(d-0). \] They work out the asymptotic behavior of eigenvalues and prove that the Weyl function is enough to determine the operator uniquely.
scientific article; zbMATH DE number 5702531
scientific article