Analysis of Pseudo-Differential Operators

伪微分算子分析

• 批准号: RGPIN-2016-05353
• 负责人: Wong, Man
• 金额: $ 1.09万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635279
• 关键词: Analysis; Pseudo; Differential; Operators

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

本文的研究是对海森堡群的次拉普拉斯算子关于中心的逆傅里叶变换所得到的扭曲拉普拉斯算子的研究的扩展。扭曲拉普拉斯算子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绿色函数。扭曲拉普拉斯算子的一个特点是它的每一个本征值都有无限重数，从而几乎不能揭示能级结构的信息。最近Gramchev，Pilipovic，Rodino和我发现，扭曲Laplacian及其