On Recovering the Sturm–Liouville Differential Operators on Time Scales

We study Sturm–Liouville differential operators on the time scales consisting of a finite number of isolated points and closed intervals. In the author's previous paper, it was established that such operators are uniquely determined by the spectral characteristics of all classical types. In the present paper, an algorithm for their recovery based on the method of spectral mappings is obtained. We also prove that the eigenvalues of two Sturm–Liouville boundary-value problems on time scales with one common boundary condition alternate.