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


inverse problems

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.

Inverse Spectral Problem for Discrete Operators in Topological Spaces

An inverse spectral problem for discrete operators of a triangular structure in topological spaces is studied. A constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions for its solvability are obtained.