Dirac systems with locally square-integrable potentials: direct and inverse problems for the spectral functions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918471217971200 |
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| author | Sakhnovich, Alexander |
| author_facet | Sakhnovich, Alexander |
| contents | We solve the inverse problems to recover Dirac systems on an interval or semiaxis from their spectral functions (matrix valued functions) for the case of locally square-integrable potentials. Direct problems in terms of spectral functions are treated as well. Moreover, we present necessary and sufficient conditions on the given distribution matrix valued function to be a spectral function of some Dirac system with a locally square-integrable potential. Interesting connections with Paley-Wiener sampling measures appear in the case of scalar spectral functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12976 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dirac systems with locally square-integrable potentials: direct and inverse problems for the spectral functions Sakhnovich, Alexander Spectral Theory Mathematical Physics Classical Analysis and ODEs Functional Analysis 34L40, 34A55, 47B15 We solve the inverse problems to recover Dirac systems on an interval or semiaxis from their spectral functions (matrix valued functions) for the case of locally square-integrable potentials. Direct problems in terms of spectral functions are treated as well. Moreover, we present necessary and sufficient conditions on the given distribution matrix valued function to be a spectral function of some Dirac system with a locally square-integrable potential. Interesting connections with Paley-Wiener sampling measures appear in the case of scalar spectral functions. |
| title | Dirac systems with locally square-integrable potentials: direct and inverse problems for the spectral functions |
| topic | Spectral Theory Mathematical Physics Classical Analysis and ODEs Functional Analysis 34L40, 34A55, 47B15 |
| url | https://arxiv.org/abs/2306.12976 |