Harmonic Analysis on Homogeneous Spaces and its Applications
| Project/Area Number |
10640171
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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 | The University of the Air |
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Principal Investigator |
KUMAHARA Keisaku The University of the Air, Department of Liberal Arts, Professor, 教養学部, 教授 (60029486)
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Takashi Tottori University, Department of Information and Knowledge Engineerings, Associate Professor, 工学部, 助教授 (90263491)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2000: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1999: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | uncertainty principle / Fourier transform / Hardy theorem / Cowling-Price theorem / Cartan motion group / motion group / semisimple Lie group / Riemannian symmetric space / カウリング・プライスの定理 / ヘルガソン・フーリエ変換 / Hardyの定理 / ウェーブレット / Fourier変換 / L^p版ハーディの定理 |
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| Research Abstract |
We studied the properties of the Fourier transforms on homogeneous spaces of Lie groups. Especially, we focussed our attention on the the uncertainty principle for Lie groups. First, we generalized the Hardy theorem for the classical Fourier transform to the Cartan motion groups. We also established an L^p-version of the Hardy theorem, which is called the Cowling-Price theorem, for general motion groups.
Next we studied the uncertainty principle for semisimple Lie groups. We proved an analogue of the Hardy theorem for connected noncompact semisimple Lie groups. The theorem can be stated by the Fourier transforms corresponding to the continuous principal series of the group. We also succeeded to prove the Cowling-Price theorem for vector bundles over Riemannian symmtric spaces and for connected noncompact semisimple Lie groups.
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Report
(4 results)
Research Products
(15 results)
