论文标题
在球形对称可逆的鳍片中，测地射线变换
The geodesic ray transform on spherically symmetric reversible Finsler manifolds
论文作者
论文摘要
我们表明，在球形对称的可逆鳍歧管上，地球射线变换是对标量函数的注入性，其中Finsler Norm可以满足HERGLOTZ条件。我们使用角度傅立叶系列将注入性问题降低到广义亚伯变换的可逆性，而通过泰勒的地球化学扩展，我们表明这些ABEL变换是注入性的。我们的结果在线性边界刚度问题上应用于鳍片歧管，尤其是在线性化弹性旅行时间断层扫描中。
We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to the invertibility of generalized Abel transforms and by Taylor expansions of geodesics we show that these Abel transforms are injective. Our result has applications in linearized boundary rigidity problem on Finsler manifolds and especially in linearized elastic travel time tomography.
