On recovering the Sturm--Liouville differential operators on time scales

Abstract

We study Sturm--Liouville differential operators on the time scales consisting of a finite number of isolated points and segments. In a previous paper it was established that such operators are uniquely determined by their spectral characteristics. 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 with one common boundary condition alternate.

References in corpus (4)

• Ambarzumyan Type Theorems on a Time Scale
• A uniqueness theorem on inverse spectral problems for the Sturm--Liouville differential operators on time scales
• Inverse problem with transmission eigenvalues for the discrete Schrödinger equation
• Recovery of the matrix quadratic differential pencil from the spectral data

Cited by in corpus (1)

• On inverse spectral problems for Sturm-Liouville differential operators on closed sets