Analysis of Pseudo-Differential Operators

本研究是在对Heisenberg群上的子拉普拉斯算子对中心进行傅里叶反变换的基础上，对扭曲拉普拉斯算子的研究进行扩展。扭曲拉普拉斯函数的特征值和特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。扭曲拉普拉斯算子的一个特殊特征是它的每一个特征值都有无限的多重性，因此几乎没有揭示能级结构的信息。最近Gramchev， Pilipovic， Rodino和我发现扭曲的拉普拉斯函数和它的乘积

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