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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.18983 |
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| _version_ | 1866912917597716480 |
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| author | Kykkänen, Antti Mishra, Rohit Kumar Sahoo, Suman Kumar |
| author_facet | Kykkänen, Antti Mishra, Rohit Kumar Sahoo, Suman Kumar |
| contents | We study a solenoidal-potential type decomposition of a symmetric $m$-tensor field in $\Rb^2$, and its implications to injectivity questions for the momentum and elastic ray transforms. For symmetric tensor fields, a general decomposition with a restriction on the dimension and order of the decomposition was proved in~\cite{Rohit_Suman}. We extend the result to dimension $2$ under a mean-zero assumption. We use the decomposition in $2$ dimensions to prove the injectivity of the momentum and elastic ray transforms. We also prove a connection between the two integral transforms for $2$-tensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18983 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A generalized Helmholtz-type decomposition of symmetric tensor fields and applications to ray transforms Kykkänen, Antti Mishra, Rohit Kumar Sahoo, Suman Kumar Analysis of PDEs We study a solenoidal-potential type decomposition of a symmetric $m$-tensor field in $\Rb^2$, and its implications to injectivity questions for the momentum and elastic ray transforms. For symmetric tensor fields, a general decomposition with a restriction on the dimension and order of the decomposition was proved in~\cite{Rohit_Suman}. We extend the result to dimension $2$ under a mean-zero assumption. We use the decomposition in $2$ dimensions to prove the injectivity of the momentum and elastic ray transforms. We also prove a connection between the two integral transforms for $2$-tensors. |
| title | A generalized Helmholtz-type decomposition of symmetric tensor fields and applications to ray transforms |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.18983 |