Necessary and sufficient conditions for the solvability of the inverse problem for Sturm–Liouville operators with a nonintegrable singularity inside a finite interval

The inverse spectral problem of recovering Sturm–Liouville operators on a finite interval with a nonintegrable Bessel-type singularity in an interior point from the given spectral data is studied. A corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions for the solvability of the inverse problem are obtained.