可定向曲面上的混合射线变换与横向射线变换
On mixed and transverse ray transforms on orientable surfaces
AI总结：
本文提出混合射线变换框架，证明不同混合射线变换的核与稳定性可相互归结，并将既有结果推广到测地射线变换螺线单射的可定向曲面。
摘要：
流形上张量场的测地射线变换、混合射线变换和横向射线变换，都可视为我们所称的混合射线变换，即测地射线变换与张量场上某个可逆线性映射的复合。我们证明，一种混合射线变换的核刻画与稳定性可归结为任意其他混合射线变换的相同性质。该方法适用于多种几何结构和射线变换，包括光线变换。特别地，我们将 de Hoop–Saksala–Zhai（2019）的研究从紧致简单曲面推广到具有螺线单射测地射线变换的可定向曲面。证明基于代数论证。
英文摘要：
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.
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