广义亚辛算子类的整表示
Integral Representations for the Class of Generalized Metaplectic Operators
摘要：
本文给出了以辛矩阵为标准变换的广义亚辛算子，即薛定谔型傅里叶积分算子（FIO）的显式积分公式.这些积分在R^d的特定线性子空间上，与基础2d x 2d辛矩阵的d x d左上方子矩阵相关。参数使用的整表示的经典metaplectic运营商获得Morsche和Oonincx在以前的文件，代数性质的辛矩阵和时频工具。作为应用，我们给出了R中任意时刻t，甚至在所谓的焦散点上，具有有界扰动的薛定谔方程的柯西问题解的具体整表示.
英文摘要：
This article gives explicit integral formulas for the so-called generalized metaplectic operators, i.e. Fourier integral operators (FIOs) of Schrödinger type, having a symplectic matrix as canonical transformation. These integrals are over specific linear subspaces of R^d, related to the d x d upper left-hand side submatrix of the underlying 2d x 2d symplectic matrix. The arguments use the integral representations for the classical metaplectic operators obtained by Morsche and Oonincx in a previous paper, algebraic properties of symplectic matrices and time-frequency tools. As an application, we give a specific integral representation for solutions to the Cauchy problem of Schrödinger equations with bounded perturbations for every instant time t in R, even in the so-called caustic points.
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