Radon transforms on homogeneous spaces and their application to harmonic analysis
| Project/Area Number |
19540208
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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 |
Global analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
KAKEHI Tomoyuki University of Tsukuba, 大学院・数理物質科学研究科, 准教授 (70231248)
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| Co-Investigator(Kenkyū-buntansha) |
ISOZAKI Hiroshi 筑波大学, 大学院・数理物質科学研究科, 教授 (90111913)
TAKEUCHI Kiyoshi 筑波大学, 大学院・数理物質科学研究科, 准教授 (70281160)
KINOXHITA Tamotsu 筑波大学, 大学院・数理物質科学研究科, 准教授 (90301077)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | ラドン変換 / 等質空間 / 対称空間 / 像の特徴付け / 反転公式 / シュレディンガー方程式 / 基本解 / 台 / 像の特徴づけ / 多重時間波動方程式 |
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| Research Abstract |
We studied Radon transforms on homogeneous spaces, and their applications to harmonic analysis. Our results are as follows. (1) We proved that the ranges of generalized matrix Radon transforms are characterized by Pfaffian type invariant differential operators. In addition, we also obtained the inversion formulas. (2) We proved that under some condition the support of the fundamental solution to the Schroedinger equation on a compact symmetric space becomes a lower dimensional subset at a rational time and that it coincides with the whole symmetric space at an irrational time.
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Report
(4 results)
Research Products
(9 results)
