Abstract

Under consideration are the operators of angular moments which map the values of generalized attenuated ray transforms (ART) into the set of symmetric \(p \)-tensor fields. The differential relations between the values of ARTs of various orders, acting on stationary or dynamic source distributions \(f \), serve as the basis for establishing the differential connections between the tensor fields of angular moments of various orders \(k \) and ranks \(p \). The particular cases are indicated allowing us to obtain some previously known results. Connections of the ARTs of order \(k \) with the problems of tomography and integral geometry as well as the established properties and connections between ARTs and angular moments can be useful as additional information when constructing the iterative algorithms for solving the problems of dynamic refraction tensor tomography.

中文翻译：

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标量$$ \ boldsymbol {3D} $$-场的衰减射线变换的角矩算子

摘要

正在考虑的是角矩算子，它们将广义衰减射线变换（ART）的值映射到对称\（p \）-张量场中。作用于平稳或动态源分布\（f \）的各种阶数的ARTs值之间的微分关系 ，为在各种阶数\（k \）和角动量的张量场之间建立微分连接的基础。排名\（p \）。指出了特殊情况，使我们可以获得一些以前已知的结果。\（k \）的ART的连接 层析成像和整体几何学的问题，以及ARTs与角矩之间已建立的特性和联系，在构造解决动态折射张量层析成像问题的迭代算法时，可以作为附加信息。