论文标题
线性化的calderón问题和指数准确的准示象，用于分析歧管
Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds
论文作者
论文摘要
在本文中，我们研究了与边界紧凑的riemannian歧管上线性化的各向异性calderón问题。这个问题表明，歧管的谐波功能对成对形成完整集。我们假设该歧管是横向各向异性的，并且横向流形是真实的分析，并且满足与相交的大地测量成对的几何形状相关的几何条件。在这种情况下，我们解决了线性的各向异性Calderón问题。几何条件不涉及地球X射线变换的注入性。我们结果证明的关键成分是横向歧管上高斯束准示象的构建，具有指数级的误差以及FBI变换的表征分析波前置集。
In this article we study the linearized anisotropic Calderón problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We assume that the manifold is transversally anisotropic and that the transversal manifold is real analytic and satisfies a geometric condition related to the geometry of pairs of intersecting geodesics. In this case, we solve the linearized anisotropic Calderón problem. The geometric condition does not involve the injectivity of the geodesic X-ray transform. Crucial ingredients in the proof of our result are the construction of Gaussian beam quasimodes on the transversal manifold, with exponentially small errors, as well as the FBI transform characterization of the analytic wave front set.
