论文标题
表面上的非亚伯X射线变换
The non-Abelian X-ray transform on surfaces
论文作者
论文摘要
本文解决了非亚伯X射线变换的简单表面上的直线性矩阵线性群体上的注射性问题。主要思想是将循环组的分解定理用于减少统一组的设置，在这种情况下，可以使用能量方法和标量塑性整合因子。我们还表明，我们的主要定理扩展以涵盖任意谎言组的案例。
This paper settles the question of injectivity of the non-Abelian X-ray transform on simple surfaces for the general linear group of invertible complex matrices. The main idea is to use a factorization theorem for Loop Groups to reduce to the setting of the unitary group, where energy methods and scalar holomorphic integrating factors can be used. We also show that our main theorem extends to cover the case of an arbitrary Lie group.
