On mixed and transverse ray transforms on orientable surfaces
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866917770880352256 |
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| author | Ilmavirta, Joonas Mönkkönen, Keijo Railo, Jesse |
| author_facet | Ilmavirta, Joonas Mönkkönen, Keijo Railo, Jesse |
| contents | The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear map on tensor fields. We show that the characterization of the kernel and the stability of a mixing ray transform can be reduced to the same properties of any other mixing ray transform. Our approach applies to various geometries and ray transforms, including the light ray transform. In particular, we extend studies in de Hoop--Saksala--Zhai (2019) from compact simple surfaces to orientable surfaces with solenoidally injective geodesic ray transform. Our proofs are based on algebraic arguments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2009_01043 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On mixed and transverse ray transforms on orientable surfaces Ilmavirta, Joonas Mönkkönen, Keijo Railo, Jesse Differential Geometry Analysis of PDEs 44A12, 65R32, 53A99 The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear map on tensor fields. We show that the characterization of the kernel and the stability of a mixing ray transform can be reduced to the same properties of any other mixing ray transform. Our approach applies to various geometries and ray transforms, including the light ray transform. In particular, we extend studies in de Hoop--Saksala--Zhai (2019) from compact simple surfaces to orientable surfaces with solenoidally injective geodesic ray transform. Our proofs are based on algebraic arguments. |
| title | On mixed and transverse ray transforms on orientable surfaces |
| topic | Differential Geometry Analysis of PDEs 44A12, 65R32, 53A99 |
| url | https://arxiv.org/abs/2009.01043 |