Geometric Analysis of Schroedinger equations on symmetric spaces
| Project/Area Number |
17K05328
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 対称空間 / 幾何解析 / シュレディンガー方程式 / 平均値作用素 / 全射性 / 合成積作用素 / 基本解 / 帯球関数 / ワイル領域 / 球関数 / 関数方程式論 / タルボット効果 |
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| Outline of Final Research Achievements |
At the beginning, the purpose of our research was to study the detailed geometric and analytical structure of the fundamental solution to the Schroedinger equation on symmetric spaces.However, through the analysis of zonal spherical functions on symmetric spaces,we found that our research is closely related to the study of the operator theoretical property of mean value operators on symmetric spaces.Therefore, we decided to focus on this subject. The result we obtained in our research program is as follows.
We consider the mean value operator to be a map from the space of smooth functions to itself. Then we proved that the mean value operator is surjective under some suitable conditions.We also obtained some related results on convolution operators.It is expected that our result will be applied to the wave equations on symmetric spaces.
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| Academic Significance and Societal Importance of the Research Achievements |
平均値作用素および関連する合成積作用素の作用素論的性質の研究はユークリッド空間上でのみ研究されており、対称空間上では主だった結果はなかった。本研究により、平均値作用素と対称空間の幾何構造との密接な関係が明らかになったことは意義がある。また、本研究により、対称空間上で研究する有効な方法が開発された点、および、対称空間上の微分方程式や調和解析を研究するための新しい方法が提供された点でも意義がある。
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Report
(6 results)
Research Products
(14 results)
