Guillarmou's Normal Operator for Magnetic and Thermostat Flows
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912793479872512 |
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| author | Muñoz-Thon, Sebastián Richardson, Sean |
| author_facet | Muñoz-Thon, Sebastián Richardson, Sean |
| contents | Guillarmou's normal operator over a closed Anosov manifold is analogous to the classical normal operator of the geodesic X-ray transform over manifolds with boundary. In this paper, we generalize this normal operator, under some dynamical assumptions, to thermostat flows as well as to the case of the magnetic flows. In particular, we show that these generalized normal operators are elliptic pseudodifferential operators of order -1 in each case. As an application, we prove a stability estimate for the magnetic X-ray transform. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Guillarmou's Normal Operator for Magnetic and Thermostat Flows Muñoz-Thon, Sebastián Richardson, Sean Analysis of PDEs Differential Geometry Dynamical Systems 37D20, 37D40, 35R30, 53C65, 37C30 Guillarmou's normal operator over a closed Anosov manifold is analogous to the classical normal operator of the geodesic X-ray transform over manifolds with boundary. In this paper, we generalize this normal operator, under some dynamical assumptions, to thermostat flows as well as to the case of the magnetic flows. In particular, we show that these generalized normal operators are elliptic pseudodifferential operators of order -1 in each case. As an application, we prove a stability estimate for the magnetic X-ray transform. |
| title | Guillarmou's Normal Operator for Magnetic and Thermostat Flows |
| topic | Analysis of PDEs Differential Geometry Dynamical Systems 37D20, 37D40, 35R30, 53C65, 37C30 |
| url | https://arxiv.org/abs/2512.23106 |