Analysis of Pseudo-Differential Operators

本研究是对海森堡群上的次拉普拉斯关于中心的逆傅立叶变换所产生的扭曲拉普拉斯的研究的推广。扭转拉普拉斯函数的本征值和本征函数是完全已知的，可以用来显式地构造热核和格林函数。扭曲拉普拉斯的一个特殊特征是，它的每个本征值都有无限的重数，因此揭示了很少关于能级结构的信息。Gramchev，Pilipovic，Rodino和我最近发现，扭曲的拉普拉斯和它的

This research is to extend the research on the twisted Laplacian that comes from taking the inverse Fourier transform of the sub-Laplacian on the Heisenberg group with respect to the center. The eigenvalues and the eigenfunctions of the twisted Laplacian are completely known and can be used to construct the heat kernel and Green function explicitly. One special feature of the twisted Laplacian is that each of its eigenvalues has infinite multiplicity, thus revealing little information about the structutre of the energy levels. It has recently been found by Gramchev, Pilipovic, Rodino and me that the product of the twisted Laplacian and its