The Light ray transform for pseudo-Euclidean metrics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908435744817152 |
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| author | Agrawal, Divyansh Stefanov, Plamen |
| author_facet | Agrawal, Divyansh Stefanov, Plamen |
| contents | We study the ray transform $L$ over null (light) rays in the pseudo-Euclidean space with signature $(n',n'')$, $n'\ge2$, $n''\ge2$. We analyze the normal operator $L'L$, derive an inversion formula, and prove stability estimates. We show that the symbol $p(ξ)$ is elliptic but singular at the light cone. We analyze $L$ as an Fourier Integral Operator as well. Finally, we compare this to the Minkowski case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Light ray transform for pseudo-Euclidean metrics Agrawal, Divyansh Stefanov, Plamen Differential Geometry Analysis of PDEs 44A12, 53C65, 35R30 We study the ray transform $L$ over null (light) rays in the pseudo-Euclidean space with signature $(n',n'')$, $n'\ge2$, $n''\ge2$. We analyze the normal operator $L'L$, derive an inversion formula, and prove stability estimates. We show that the symbol $p(ξ)$ is elliptic but singular at the light cone. We analyze $L$ as an Fourier Integral Operator as well. Finally, we compare this to the Minkowski case. |
| title | The Light ray transform for pseudo-Euclidean metrics |
| topic | Differential Geometry Analysis of PDEs 44A12, 53C65, 35R30 |
| url | https://arxiv.org/abs/2502.13684 |