论文标题
非阳性曲率中张量断层扫描的急剧稳定性估计值
A sharp stability estimate for tensor tomography in non-positive curvature
论文作者
论文摘要
我们考虑在紧凑型磁铁张量场上作用于紧凑的歧管上的地理X射线变换，简单地连接了严格的凸边界和非阳性曲率。我们建立了$ l^2 \ mapsto h^{1/2} _ {t} $的稳定性估计值，其中$ h^{1/2} _ {t} $ - 使用地理学的自然参数化作为初始边界点和intoming方向（fan-beam deemotry）定义了空间；仅使用边界处的切向导数。证明基于pestov身份，其边界项以频率定位。
We consider the geodesic X-ray transform acting on solenoidal tensor fields on a compact simply connected manifold with strictly convex boundary and non-positive curvature. We establish a stability estimate of the form $L^2\mapsto H^{1/2}_{T}$, where the $H^{1/2}_{T}$-space is defined using the natural parametrization of geodesics as initial boundary points and incoming directions (fan-beam geometry); only tangential derivatives at the boundary are used. The proof is based on the Pestov identity with boundary term localized in frequency.
