| Project/Area Number |
11440037
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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 |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
ARAI Hitoshi The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (10175953)
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| Co-Investigator(Kenkyū-buntansha) |
KANJIN Yuichi Kanazawa University, Faculty of Sciences, Professor, 工学部, 教授 (50091674)
OZAWA Toru Hokkaido University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (70204196)
YAJIMA Kenji The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (80011758)
MORITO Shinya Nara women's University, Faculty of Sciences, lecturer, 理学部, 講師 (30273832)
NOGUCHI Junjiro The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (20033920)
黒田 成俊 学習院大学, 理学部, 教授 (20011463)
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| Project Period (FY) |
1999 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥10,000,000 (Direct Cost: ¥10,000,000)
Fiscal Year 2001: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2000: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 1999: ¥3,700,000 (Direct Cost: ¥3,700,000)
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| Keywords | Harmonic functions / Negatively curved manifolds / Schrodinger equations / Nonlinear Schrodinger equations / Hardy spaces / Fourier multiplier / F.B.I transform / Bloch function / 非線形シュレーディンガー方程式 / F.B.I.変換 / 負曲率多様体上の調和解析 / 離散ハーディー空間 / 非線形波動方程式 / 非線形クライン・ゴルドン方程式 / ブロック調和写像 / 複素幾何 / Hardy空間 / Schrodinger方程式 / 複素多様体 / 実解析学 / 非線型Schrodinger方程式 / Green関数 |
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| Research Abstract |
Arai studied harmonic analysis on negatively curved manifolds. Let M be a complete, simply connected Riemannian manifold whose sectional curvatures K_M satisfy -∞ < -k^2_2 【less than or equal】 K_M 【less than or equal】 -k^2_1 < 0, where k_1 and k_2 are positive constants. Arai obtained several results on elliptic harmonic functions on M. In particular he established fundamental part of harmonic analysis on M by proving theorems related to Hardy spaces, BMO, VMO, Carleson measures, Green's potential. As applications, he also studied Bloch function theory on manifolds and the regularity problem of degenerate harmonic measures. Ozawa studied by using real variable method nonlinear Schrodinger equations, nonlinear wave equations and nonlinear Krein-Gordon equations. Yajima obtained some results on the fundamental solutions of Schrodinger equations. Kanjin proved Paley's inequality for Jacobi expansions and studied the Hausdorff operator acting on real Hardy spaces.
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