ℝ³中二阶张量场的受限混合射线变换的微局部反演
Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in $\mathbb{R}^3$
AI总结：
针对ℝ³中穿过固定曲线γ的直线上的二阶张量场受限混合射线变换，本文用微局部方法证明其可在核、平滑项及已知奇异项意义下反演恢复张量场。
摘要：
本文研究作用于三维欧几里得空间中二阶张量场的受限混合射线变换，并利用微局部技术证明该积分变换的可逆性。这里，混合射线变换被限制在穿过ℝ³中满足特定几何条件的固定曲线γ的直线上。本文的主要定理表明，二阶张量场可由其受限混合射线变换恢复，误差至多为该变换的核、一个平滑项以及一个已知奇异项。
英文摘要：
In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray transform is restricted over lines passing through a fixed curve $γ$ in $\mathbb{R}^3$ satisfying certain geometric conditions. The main theorem of the article shows that a second-order tensor field can be recovered from its restricted mixed-ray transform up to the kernel of the transform, a smoothing term, and a known singular term.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
