论文标题
Gabor波包的分散，扩散和稀疏性，用于Metapclect和Schrödinger操作员
Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators
论文作者
论文摘要
在最近的论文中，已经对几种类型运算符的相位空间表示的稀疏性属性进行了广泛的研究，包括伪差异，傅立叶积分和元容器运算符，并应用于Schrödinger-type Evolution Evolution Evolution Evolution方程的时间频率分析。已经证明，此类操作员通过Gabor波数据包近似对角线。虽然预计后者会经历一些传播现象，但在上述结果中没有记录此问题。在本文中，我们证明了对元容器的Gabor矩阵的精致估计，也是广义类型的，其中稀疏性，扩散和分散性能都引人注目。我们为Schrödinger方程的奇异性传播提供了应用。
Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent papers, including pseudodifferential, Fourier integral and metaplectic operators, with applications to time-frequency analysis of Schrödinger-type evolution equations. It has been proved that such operators are approximately diagonalized by Gabor wave packets. While the latter are expected to undergo some spreading phenomenon, there is no record of this issue in the aforementioned results. In this paper we prove refined estimates for the Gabor matrix of metaplectic operators, also of generalized type, where sparsity, spreading and dispersive properties are all noticeable. We provide applications to the propagation of singularities for the Schrödinger equation.
