1998 Fiscal Year Final Research Report Summary
Pseudodifferential Operators and Schrodinger Equations
| Project/Area Number |
09440060
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | OSAKA UNIVERSITY |
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Principal Investigator |
NAGASE Michihiro Osaka University, Grad.Sch.of Sci., Professor, 大学院・理学研究科, 教授 (70034733)
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| Co-Investigator(Kenkyū-buntansha) |
KOTANI Shinnichi Osaka University, Grad.Sch.of Sci., Professor, 大学院・理学研究科, 教授 (10025463)
SUZUKI Takashi Osaka University, Grad.Sch.of Sci., Professor, 大学院・理学研究科, 教授 (40114516)
IBUKIYAMA Tomoyoshi Osaka University, Grad.Sch.of Sci., Professor, 大学院・理学研究科, 教授 (60011722)
KOISO Norihito Osaka University, Grad.Sch.of Sci., Professor, 大学院・理学研究科, 教授 (70116028)
NISHITANI Tatsuo Osaka University, Grad.Sch.of Sci., Professor, 大学院・理学研究科, 教授 (80127117)
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| Project Period (FY) |
1997 – 1998
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| Keywords | symbol / Wigner distribution / compact operators / spectral inveriance / quantized Hamiltonian / Potential |
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| Research Abstract |
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.
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