论文标题
具有部分数据的一型X射线断层扫描
X-ray tomography of one-forms with partial data
论文作者
论文摘要
如果所有符合小的开放式套件的单一形式的积分消失并在此组中关闭形式，则在整个欧几里得空间中，单一形式是精确的。我们为单一形式的X射线变换的正常运算符获得了独特的延续结果，这导致了我们对部分数据结果的两个证明之一。我们的证明适用于紧凑型的共同值得评估的分布。
If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.
