SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5675-5702, January 2020.
On simple geodesic disks of constant curvature, we derive new functional relations for the geodesic X-ray transform, involving a certain class of elliptic differential operators whose ellipticity degenerates normally at the boundary. We then use these relations to derive sharp mapping properties for the X-ray transform and its corresponding normal operator. Finally, we discuss the possibility of theoretically rigorous regularized inversions for the X-ray transform when defined on such manifolds.

中文翻译：

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等曲率圆盘上的函数关系，清晰的映射特性和X射线变换的正则化

SIAM数学分析期刊，第52卷，第6期，第5675-5702页，2020
年1月。在恒定曲率的简单测地盘上，我们推导了测地X射线变换的新函数关系，其中涉及特定种类的椭圆微分算子椭圆率通常在边界处退化。然后，我们使用这些关系来为X射线变换及其对应的法线算符导出清晰的映射属性。最后，我们讨论了在这样的流形上定义X射线变换的理论上严格的正规化反演的可能性。