论文标题
X射线在渐近圆锥形空间上转换
The X-ray transform on asymptotically conic spaces
论文作者
论文摘要
在本文的一部分基于Zachos的博士学位论文中，我们表明，在一类渐近圆锥形歧管上，地球X射线变换在无穷大附近是可逆的，其中包括欧几里得空间的扰动。特别是某些类型的共轭点。此外，在全球凸叶条件下，转换在全球范围内是可逆的。 除了Uhlmann和Vasy介绍的方法之外，关键的分析工具是引入新的pseudoDifferential Operator代数，我们将其命名为1-Cusp代数及其半经典版本。
In this paper, partly based on Zachos' PhD thesis, we show that the geodesic X-ray transform is stably invertible near infinity on a class of asymptotically conic manifolds which includes perturbations of Euclidean space. In particular certain kinds of conjugate points are allowed. Further, under a global convex foliation condition, the transform is globally invertible. The key analytic tool, beyond the approach introduced by Uhlmann and Vasy, is the introduction of a new pseudodifferential operator algebra, which we name the 1-cusp algebra, and its semiclassical version.
