On Inverse Spectral Problems for Sturm-Liouville Differential Operators on Closed Sets

We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred to as time scales and often appear in modelling various real-world processes. Depending on the set structure, such operators unify both differential and difference operators. The time scales under consideration consist of a finite number of non-intersecting segments. We obtain properties of the spectral characteristics and prove uniqueness theorems for inverse problems of recovering the operator from two types of spectral data: the Weyl function, as well as the spectra of two boundary value problems for one and the same Sturm-Liouville equation on the time scale with one common boundary condition.