论文标题
注入性和第一个$（k+1）的范围描述$积分力矩在$ \ mathbb {r}^n $中以$ m $ -tensor字段转换
Injectivity and range description of first $(k+1)$ integral moment transforms over $m$-tensor fields in $\mathbb{R}^n$
论文作者
论文摘要
在这项工作中，我们证明了对等级$ M $对称张量场的新分解结果，该张量概括了张张量场的众所周知的螺线管和潜在分解。然后，该分解用于描述内核，并证明第一个$（k+1）的注射率结果（k+1）$ symmetric $ m $ m $ -tensor字段的积分矩转换为$ \ mathbb {r}^n $。此外，我们还为第一个$（k+1）$积分时刻转换在约翰方程式方面。
In this work, we prove a new decomposition result for rank $m$ symmetric tensor fields which generalizes the well known solenoidal and potential decomposition of tensor fields. This decomposition is then used to describe the kernel and to prove an injectivity result for first $(k+1)$ integral moment transforms of symmetric $m$-tensor fields in $\mathbb{R}^n$. Additionally, we also present a range characterization for first $(k+1)$ integral moment transforms in terms of the John's equation.
