Uniform stability for the Hochstadt-Lieberman problem
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914971564113920 |
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| author | Bondarenko, Natalia P. |
| author_facet | Bondarenko, Natalia P. |
| contents | In this paper, we prove the uniform stability of the Hochstadt-Lieberman problem, which consists in the recovery of the Sturm-Liouville potential on a half-interval from the spectrum and the known potential on the other half-interval. For this purpose, we reduce the half-inverse problem to the complete one for the unknown potential. Our method relies on the uniform stability for the direct and inverse Sturm-Liouville problems, for recovering sine-type functions from their zeros, and the uniform boundedness of Riesz bases of sines and cosines. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_10326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform stability for the Hochstadt-Lieberman problem Bondarenko, Natalia P. Spectral Theory 34A55 34B05 34B09 34L40 In this paper, we prove the uniform stability of the Hochstadt-Lieberman problem, which consists in the recovery of the Sturm-Liouville potential on a half-interval from the spectrum and the known potential on the other half-interval. For this purpose, we reduce the half-inverse problem to the complete one for the unknown potential. Our method relies on the uniform stability for the direct and inverse Sturm-Liouville problems, for recovering sine-type functions from their zeros, and the uniform boundedness of Riesz bases of sines and cosines. |
| title | Uniform stability for the Hochstadt-Lieberman problem |
| topic | Spectral Theory 34A55 34B05 34B09 34L40 |
| url | https://arxiv.org/abs/2410.10326 |