On Uniqueness Theorems for the Inverse q-Sturm-Liouville problems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914007458250752 |
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| author | Gawish, F. A. Mansour, Z. S. |
| author_facet | Gawish, F. A. Mansour, Z. S. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_04287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Uniqueness Theorems for the Inverse q-Sturm-Liouville problems Gawish, F. A. Mansour, Z. S. Classical Analysis and ODEs Functional Analysis 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. |
| title | On Uniqueness Theorems for the Inverse q-Sturm-Liouville problems |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2411.04287 |