1988 Fiscal Year Final Research Report Summary
Harmonic Analysis on Symmetric Spaces
| Project/Area Number |
62460004
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | University of Tokyo, Faculty of Science, Department of Mathematics |
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Principal Investigator |
OSHIMA Toshio University of Tokyo, Faculty of Science, Professor, 理学部, 教授 (50011721)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Toshiyuki University of Tokyo, Faculty of Science, Assistant, 理学部, 助手 (80201490)
TOSE Nobuyuki University of Tokyo, Faculty of Science, Assistant, 理学部, 助手 (00183492)
KATAOKA Kiyoomi University of Tokyo, Faculty of Science, Associate Professor, 理学部, 助教授 (60107688)
IHARA Yasutaka University of Tokyo, Faculty of Science, Professor, 理学部, 教授 (70011484)
HATTORI Akio University of Tokyo, Faculty of Science, Professor, 理学部, 教授 (80011469)
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| Project Period (FY) |
1987 – 1988
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| Keywords | Symmetric space / Homogeneous space / Harmonic analysis / Unitary representation / Lie group / Boundary value / 代数解析 |
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| Research Abstract |
1. Under this project, Oshima organized a simposium at University of Tokyo on January 1988 and also summer seminars at Institute of Vocational training on August 1988 and August 1989, and we discussed the present stage of the project and its future development.
2. Oshima published several important results which will be used to obtain the main aim in harmonic analysis on semisimple symmetric spaces, the Plancherel formula. They are as follows: Oshima realized a smooth imbedding of the symmetric space in a compact manifold and by using it, Oshima constructed boundary value maps for eigenfunctions of the invariant differential operators and discovered that the asymptotic of the eigenfunctions at infinity are characterized by a simple geometric structure. By the same method Oshima proved a certain boundedness of unitarizable Harish-Chandra modules realized on a homogeneous space.
3. Kobayashi calculated the spectra of the Laplacian on a homogeneous space which is a fibre bundle over Riemann
… More
ian symmetric space. This gives a counter example of a conjecture given by Sunada. Kobayashi also proved the existence of uniform lattices in several series of semisimple symmetric spaces.
4. Hattori proved a certain vanishing theorem of Kodaira type for a line bundle over a almost complex manifold with S^1-action when the dimension of the manifold is small.
5. Masuda shows the existence and boundedness of solutions for some reaction-diffusion systems posed by Gierer-Meinhard as mathematical models of biological formation.
6. Ihara studied the absolute Galois group over the rational number field and its natural actions on the completion of the fundamental group of a certain algebraic manifold. Ihara is making clear that the actions give sufficiently general non-abelian representations of the Galois group and obtained several applications to number theory.
7. Kataoka and Tose extended the theory of microlocal propagation of regularities for microlocal hyperbolic boundary value problems originated by Sjostrand. Their result also contains and existence theorem of the solutions. Less
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Research Products
(11 results)
