Pseudo-differential analysis on stratified groups

该项目的目的是在分层群体的背景下进行一些明确的分析。第一个目的是将Heisenberg群上可用的伪微分分析推广到Angel群和Cartan群的背景下。这将包括不变矢量场和次拉普拉斯量的无穷小表示的显式表达式，以及Kohn-Nirenberg和Weyl型量子化的版本，并应用于Gevrey空间和波型方程的分析。因此，人们的目标是将其扩展到更一般的分层群体的背景下，并从这些具体的案例中获得明确的景象。

In aim of the project is to carry out some explicit analysis in the context of stratified groups. The first aim is to extend the pseudo-differential analysis explicitly available on the Heisenberg group to the context of Angel and Cartan groups. This will include explicit expressions for the infinitesimal representations of invariant vector fields and the sub-Laplacian, versions of the Kohn-Nirenberg and Weyl type quantizations, with applications to the analysis of Gevrey spaces and wave type equations. Consequently, one aims at extending this to the setting of more general stratified groups aided by the explicit sights obtained from these specific cases.