论文标题
在混合和横向射线上转换可定向的表面
On mixed and transverse ray transforms on orientable surfaces
论文作者
论文摘要
地球射线变换，混合射线变换和张量场在歧管上的横向射线变换都可以看作是我们所谓的混合射线变换，地球射线变换的组成以及张量场上的可逆线性映射。我们表明，可以将内核的表征和混合射线变换的稳定性降低到任何其他混合射线变换的相同特性。我们的方法适用于各种几何形状和射线变换，包括光线变换。特别是，我们将De Hoop-saksala-Zhai（2019）的研究从紧凑的简单表面扩展到具有螺线管内镜的大地射线变换的可定向表面。我们的证明基于代数论点。
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.
