零阶符号势在径向点附近的微局域传播和散射
Microlocal propagation near radial points and scattering for symbolic potentials of order zero
摘要：
本文发展了$H=Δ_g+V$的散射和谱理论，其中$Δ_g$是紧致流形$X$上关于散射度量$g$的拉普拉斯算子，$V\in C^\infty(X)$是实数，这推广了我们以前在二维情形下的结果.包括在这类运营商是扰动的拉普拉斯算子在欧几里得空间的潜力齐次的零度附近无穷大。几何散射理论的许多特殊结构可以追溯到基本经典系统的径向点的发生;在这些点上的微局部分析的一般框架构成了本文的主要部分。
英文摘要：
In this paper, the scattering and spectral theory of $H=Δ_g+V$ is developed, where $Δ_g$ is the Laplacian with respect to a scattering metric $g$ on a compact manifold $X$ with boundary and $V\in C^\infty(X)$ is real; this extends our earlier results in the two-dimensional case. Included in this class of operators are perturbations of the Laplacian on Euclidean space by potentials homogeneous of degree zero near infinity. Much of the particular structure of geometric scattering theory can be traced to the occurrence of radial points for the underlying classical system; a general framework for microlocal analysis at these points forms the main part of the paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
