оператор Штурма–Лиувилля

Numerical Solution of Inverse Spectral Problems for Sturm–Liouville Operators with Discontinuous Potentials

Authors: Efremova L. S.

We consider Sturm–Liouville differential operator with potential having a finite number of simple discontinuities. This paper is devoted to the numerical solution of such inverse spectral problems. The main result of this work is a procedure that is able to recover both the points of discontinuities as well as the heights of the jumps. Following, using these results, we may apply a suitable numerical method (for example, the generalized Rundell–Sacks algorithm with a special form of the reference potential) to reconstruct the potential more precisely.

Inverse problem for Sturm–Liouville operator on the half-line having nonintegrable singularity in an interior point

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

Necessary and Sufficient Conditions for the Solvability of the Inverse Problem for Sturm–Liouville Operators with a Nonintegrable Singularity Inside a Finite Interval

Authors: Fedoseev A. E.

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.