Analysis of Pseudo-Differential Operators

点击翻译按钮获取中文摘要

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