Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

Sturm–Liouville operators

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.