Radon Transform over Tensor Fields: Injectivity, Range, and Unique Continuation Principle
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915897456721920 |
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| author | Mishra, Rohit Kumar Thakkar, Chandni |
| author_facet | Mishra, Rohit Kumar Thakkar, Chandni |
| contents | A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms. In this paper, we study all these aspects for Radon transforms acting on symmetric $m$-tensor fields in $\mathbb{R}^n$. Our results show that these transforms admit a coherent analytic structure, extending several key features of the classical Radon transform and tensor ray transforms to a broader geometric setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_27638 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Radon Transform over Tensor Fields: Injectivity, Range, and Unique Continuation Principle Mishra, Rohit Kumar Thakkar, Chandni Analysis of PDEs 44A12, 44A30, 46F12, 47G10 A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms. In this paper, we study all these aspects for Radon transforms acting on symmetric $m$-tensor fields in $\mathbb{R}^n$. Our results show that these transforms admit a coherent analytic structure, extending several key features of the classical Radon transform and tensor ray transforms to a broader geometric setting. |
| title | Radon Transform over Tensor Fields: Injectivity, Range, and Unique Continuation Principle |
| topic | Analysis of PDEs 44A12, 44A30, 46F12, 47G10 |
| url | https://arxiv.org/abs/2603.27638 |