Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in $\mathbb{R}^3$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912028711452672 |
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| author | Thakkar, Chandni |
| author_facet | Thakkar, Chandni |
| contents | In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray transform is restricted over lines passing through a fixed curve $γ$ in $\mathbb{R}^3$ satisfying certain geometric conditions. The main theorem of the article shows that a second-order tensor field can be recovered from its restricted mixed-ray transform up to the kernel of the transform, a smoothing term, and a known singular term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in $\mathbb{R}^3$ Thakkar, Chandni Analysis of PDEs 35A22, 35S30, 46F12 In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray transform is restricted over lines passing through a fixed curve $γ$ in $\mathbb{R}^3$ satisfying certain geometric conditions. The main theorem of the article shows that a second-order tensor field can be recovered from its restricted mixed-ray transform up to the kernel of the transform, a smoothing term, and a known singular term. |
| title | Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in $\mathbb{R}^3$ |
| topic | Analysis of PDEs 35A22, 35S30, 46F12 |
| url | https://arxiv.org/abs/2409.09341 |