论文标题
圆锥形流形和应用于schrödinger方程的半古典分解
The Semiclassical Resolvent on Conic Manifolds and Application to Schrödinger Equations
论文作者
论文摘要
在本文中，我们将在具有单锥尖端的非产物锥歧管上的光谱附近的高能量构建Laplacian的分解。在微隔离上，分解核是B-peudodivferential运算符的总和，散射伪差算子和相交的legendrian分布。作为一种应用，我们应在具有多个非产物圆锥奇点的非压缩歧管上建立Schrödinger方程的Strichartz估计值。
In this article, we shall construct the resolvent of Laplacian at high energies near the spectrum on non-product conic manifolds with a single cone tip. Microlocally, the resolvent kernel is the sum of b-pseudodifferential operators, scattering pseudodifferential operators and intersecting Legendrian distributions. As an application, we shall establish Strichartz estimates for Schrödinger equations on non-compact manifolds with multiple non-product conic singularities.
