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arXiv · 2411.04287

On Uniqueness Theorems for the Inverse q-Sturm-Liouville problems

F. A. Gawish·Z. S. Mansour
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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.

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BibTeXRIS

F. A. Gawish, Z. S. Mansour. 2024-11-06. On Uniqueness Theorems for the Inverse q-Sturm-Liouville problems. https://arxiv.org/abs/2411.04287

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