2010 Fiscal Year Final Research Report
Pseudodifferential Operators and Geometric Analysis
| Project/Area Number |
20540151
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
CHIHARA Hiroyuki Tohoku University, 理工学研究科(理学系), 教授 (70273068)
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| Research Collaborator |
ONODERA Eiji 高知大学, 自然科学系, 講師 (70532357)
KAIZUKA Koichi 東北大学, 大学院・博士後期課程在学, 日本学術振興会特別研究員DC
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| Project Period (FY) |
2008 – 2010
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| Keywords | 擬微分作用素 / Bargmann変換 / Berezin-Toeplitz作用素 / Schr-dinger写像 / 分散型偏微分方程式 / 初期値問題 |
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| Research Abstract |
The purpose of this project is to present sophisticated methods of analysis on curved spaces. Two of our main results are the following. First, we significantly improved the known facts on Berezin-Toeplitz operators acting on the image of a certain Fourier integral operators with a complex phase. Secondly, we studied the initial value problem for the Schrodinger map flow of a Riemannian manifold to an almost Kahler manifold. We clarified the meaning of the assumption of the Kahler property of the target space in all the preceding results, and succeeded in dropping this assumption by introducing pseudodifferential calculus on induced bundle associated with a map between Riemannian manifolds.
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