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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.08339 |
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| _version_ | 1866916735058182144 |
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| author | Belishev, M. I. Mikhaylov, V. S. |
| author_facet | Belishev, M. I. Mikhaylov, V. S. |
| contents | The boundary control (BC-) method is an approach to inverse problems based upon their deep relations to control and system theory. We show that the classical integral equations of inverse problem theory (Gelfand-Levitan, Krein and Marchenko equations) can be derived in the framework of the BC-method in a unified way. Namely, to solve each of these equations is in fact to solve a relevant boundary control problem, whereas its solution is determined by the inverse data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified approach to classical equations of inverse problem theory Belishev, M. I. Mikhaylov, V. S. Analysis of PDEs Spectral Theory The boundary control (BC-) method is an approach to inverse problems based upon their deep relations to control and system theory. We show that the classical integral equations of inverse problem theory (Gelfand-Levitan, Krein and Marchenko equations) can be derived in the framework of the BC-method in a unified way. Namely, to solve each of these equations is in fact to solve a relevant boundary control problem, whereas its solution is determined by the inverse data. |
| title | Unified approach to classical equations of inverse problem theory |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2505.08339 |