The Geodesic X-ray Transform with a $$GL(n,\mathbb {C})$$-Connection
The Geodesic X-ray Transform with a $$GL(n,\mathbb {C})$$-Connection
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具有 $$GL(n,mathbb {C})$$-连接的测地线 X 射线变换
DOI：
10.1007/s12220-017-9931-z
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Monard F
中科院分区：
文献类型：
--
作者：
Monard F
我们推导了在简单黎曼曲面上定义的一系列具有连接的测地射线变换的重建公式。这些公式提供了在恒定曲率度量的邻域中所有此类变换的单射性以及曲率接近于零的非酉连接。如果某些 Fredholm 方程在没有连接的情况下是单射的，那么对于任何足够平滑的连接乘以复数参数，相应的变换对于离散集之外的该参数的所有值都是单射的。还提供了范围特征。
We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of all such transforms in a neighborhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equations are injective in the absence of connection, then for any smooth enough connection multiplied by a complex parameter, the corresponding transform is injective for all values of that parameter outside a discrete set. Range characterizations are also provided.