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Pseudodifferential Operators and Schrodinger Equations

伪微分算子和薛定谔方程

基本信息

批准号：
09440060
负责人：
NAGASE Michihiro
金额：
$ 7.36万
依托单位：
OSAKA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

The purpose of the present research project is to investigate the application of pseudodifferential operators to the theory of Schrrodinger equations. There has already been many research works in this subject. In this project we investigate mainly the spectral theory of Schrodinger operators by using the theory of pseudodifferential operators. In the theory of pseudodifferential operators we obtained boundedness theorems and compactness of pseudodifferential operators and also we got the results for sharp form of Garding's inequality.Our project has many investigators and the subject which we treated is very wide, so our member attended many meetings and workshop about partial differential equations, pseudodifferential operators and mathematical phisics.Moreover we invited Professor E.Schrohe from Potzdam, Professor C.Heil from Georgia Thec., Professor H.Triebel from Yena and so on. They visited us for reviewing our research and gave several interesting talks and they were very useful for our research. We get some results on the invariance of spectral of the pseudodifferential operators which arise from the quantized Hamiltonian with magnetic potentials, which are closely related to the work of Professor Schrohe. Moreover we get some results on the muti-dimensional multi-wavelet, the result which comes from the representations of pseudidifferen-tial operators by using the Wigner distributions.

本研究的目的是研究拟微分算子在薛定谔方程理论中的应用。在这个课题上已经有了很多研究工作。在这个项目中，我们主要利用伪微分算子理论来研究薛定谔算子的谱理论。在拟微分算子理论中，我们得到了拟微分算子的有界性和紧性，也得到了Garding不等式的尖锐形式的结果。我们的项目有很多研究人员，我们所处理的主题非常广泛，所以我们的成员参加了许多关于偏微分方程、拟微分算子和数学物理的会议和研讨会。此外，我们邀请了来自波茨坦的E.Schrohe教授，来自格鲁吉亚的C.Heil教授，来自Yena的H.Triebel教授等。他们拜访了我们，回顾了我们的研究，并做了几次有趣的演讲，这些演讲对我们的研究非常有用。我们得到了一些与Schrohe教授的工作密切相关的结果，这些结果都是由带磁势的量子化哈密顿量所产生的拟微分算子谱的不变性。此外，我们还得到了多维多小波的一些结果，这些结果是由拟微分算子用Wigner分布表示的。