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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.10753 |
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| _version_ | 1866913316819959808 |
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| author | Mishra, Rohit Kumar Sahoo, Suman Kumar Thakkar, Chandni |
| author_facet | Mishra, Rohit Kumar Sahoo, Suman Kumar Thakkar, Chandni |
| contents | In this article, we study various aspects of the mixed ray transform of $(k + \ell)$-tensor fields that are symmetric in its first $k$ and last $\ell$ indices. As a first result, we derive an inversion algorithm to recover the solenoidal part of the unknown tensor field using the normal operator of the mixed ray transform. Next, we establish a set of unique continuation results. In addition to these, we discuss the range characterization of the mixed ray transform as the final result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in $\mathbb{R}^2$ Mishra, Rohit Kumar Sahoo, Suman Kumar Thakkar, Chandni Analysis of PDEs In this article, we study various aspects of the mixed ray transform of $(k + \ell)$-tensor fields that are symmetric in its first $k$ and last $\ell$ indices. As a first result, we derive an inversion algorithm to recover the solenoidal part of the unknown tensor field using the normal operator of the mixed ray transform. Next, we establish a set of unique continuation results. In addition to these, we discuss the range characterization of the mixed ray transform as the final result. |
| title | Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in $\mathbb{R}^2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.10753 |