论文标题
渐近圆锥空间上的紧张X射线转换
The tensorial X-ray transform on asymptotically conic spaces
论文作者
论文摘要
在本文中，我们显示了在渐近圆锥形歧管上的一种形式和2张量的大地X射线变换的可逆性，直到自然障碍物，从而允许存在某些类型的共轭点。我们使用1-CUSP伪数算子代数及其半经典叶面版本由Vasy和Zachos引入和使用，后者在功能上显示出相同类型的可逆性。 与功能上的X射线变换相比，紧张X射线变换的可逆性的并发症是由由“潜在张量”组成的变换的天然内核引起的。我们通过安排修改的螺线管仪条件来克服这一点，在该条件下，我们具有X射线变换的可逆性。
In this paper we show the invertibility of the geodesic X-ray transform on one forms and 2-tensors on asymptotically conic manifolds, up to the natural obstruction, allowing existence of certain kinds of conjugate points. We use the 1-cusp pseudodifferential operator algebra and its semiclassical foliation version introduced and used by Vasy and Zachos, who showed the same type invertibility on functions. The complication of the invertibility of the tensorial X-ray transform, compared with X-ray transform on functions, is caused by the natural kernel of the transform consisting of `potential tensors'. We overcome this by arranging a modified solenoidal gauge condition, under which we have the invertibility of the X-ray transform.
