On Uniqueness Theorems for the Inverse q-Sturm-Liouville problems
Classical Analysis and ODEs
2025-08-28 v2 Functional Analysis
Abstract
We establish two theorems that illustrate the uniqueness of inverse q-Sturm-Liouville problems based on a specified set of spectral data. The first uniqueness theorem employs the method of transformation operators to provide a q-analog of the Levinson-Marchenko uniqueness theorem. The second uniqueness theorem is a q-analog of the Ashrafyan uniqueness theorem. We introduced a q-analog of the Gelfand-Levitan approach, which involves converting q-difference operators into q-integral operators to prove the theorem.
Keywords
Cite
@article{arxiv.2411.04287,
title = {On Uniqueness Theorems for the Inverse q-Sturm-Liouville problems},
author = {F. A. Gawish and Z. S. Mansour},
journal= {arXiv preprint arXiv:2411.04287},
year = {2025}
}