An Inverse Problem for Sturm-Liouville Operators on the Half-line Having Bessel-type Singularity in an Interior Point

TL;DR

This paper addresses the inverse problem of reconstructing Sturm-Liouville operators with Bessel-type singularities inside the domain from Weyl functions, providing uniqueness, solvability conditions, and a constructive solution method.

Contribution

It introduces a new approach for solving inverse Sturm-Liouville problems with interior Bessel singularities, including uniqueness and constructive solution procedures.

Findings

Proved a uniqueness theorem for the inverse problem.

Established necessary and sufficient conditions for solvability.

Developed a constructive method for reconstructing the operator.

Abstract

We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.