A uniqueness theorem on inverse spectral problems for the Sturm--Liouville differential operators on time scales

TL;DR

This paper establishes a uniqueness theorem for inverse spectral problems of Sturm--Liouville operators on time scales, unifying differential and difference operators, and providing spectral property analysis including eigenvalue asymptotics.

Contribution

It introduces a uniqueness theorem for recovering Sturm--Liouville operators on time scales from spectral data, combining differential and difference operator frameworks.

Findings

Spectral characteristics of operators are thoroughly analyzed.

Asymptotic formulas for eigenvalues and weight numbers are derived.

A uniqueness theorem for inverse problems on time scales is proved.

Abstract

In the paper, Sturm--Liouville differential operators on time scales consisting of a finite number of isolated points and segments are considered. Such operators unify differential and difference operators. We obtain properties of their spectral characteristics including asymptotic formulae for eigenvalues and weight numbers. Uniqueness theorem is proved for recovering the operators from the spectral characteristics.