Harmonic Analysis on Symmetric Spaces

对称空间的调和分析

• 批准号: 62460004
• 负责人: OSHIMA Toshio
• 金额: $ 3.46万
• 依托单位: University of Tokyo, Faculty of Science, Department of Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1987
• 资助国家: 日本
• 起止时间: 1987 至 1988
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-62460004/
• 关键词: Symmetric space; Homogeneous space; Harmonic analysis; Unitary representation; Lie group; Boundary value; 代数解析; 半単純リー群; 境界値問題; 主系列表現; 離散系列表現; 半単純対称空間

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

1.在该项目下，大岛于1988年1月在东京大学举办了一次模拟研讨会，并于1988年8月和1989年8月在职业训练学院举办了夏季研讨会，我们讨论了该项目的现阶段及其未来发展。大岛出版了几个重要的成果，将用于获得主要目标调和分析半单对称空间，Plancherel公式。它们是：Oshima实现了对称空间在紧致流形上的光滑嵌入，并利用它构造了不变微分算子的本征函数的边值映射，发现了本征函数在无穷远处的渐近性具有简单的几何结构。Oshima用同样的方法证明了齐性空间上实现的酉化Harish-Chandra模的有界性.小林计算了黎曼上纤维丛齐性空间上拉普拉斯算子的谱 ...更多信息 ian对称空间这给出了一个反例的猜想所给予的Sunada。小林还证明了几类半单对称空间中一致格的存在性. Hattori证明了几乎复流形上具有S^1-作用的线丛在维数较小时的科代拉型消失定理.增田证明了由Gierer-Meinhard提出的作为生物形成数学模型的一些反应扩散系统解的存在性和有界性.伊原研究了绝对伽罗瓦群的有理数领域及其自然行动的完成基本组的一定代数流形。Ihara清楚地表明，行动给予足够普遍的非阿贝尔表示的伽罗瓦群，并获得了几个应用数论。7. Kataoka和Tose将微局部传播理论推广到Sjostrand提出的微局部双曲边值问题。其结果也包含了解的存在性定理.少

项目成果

Toshio Oshima: Advanced Studies in Pure Math.14. 561-601 (1988)

大岛敏夫：纯数学高级研究.14。

Toshiyuki,Kobayashi;T.Sunada;K.Ono: Forum Mathematicum. 1. 69-79 (1989)

Toshiyuki,Kobayashi;T.Sunada;K.Ono：数学论坛。

Toshio,Oshima: Advanced Studies in Pure Math.14. 561-601 (1988)

Toshio，Oshima：纯数学高级研究.14。

Yasatake,Ihara: Ann.of Math. 128. 271-293 (1988)

Yasatake，Ihara：数学安。

Toshio Oshima: "A realization of semisimple symmetric spaces and construction of boundary value maps" Advanced Studies in Pure Math.14. 603-650 (1988)

Toshio Oshima：“半简单对称空间的实现和边值图的构造”纯数学高级研究.14。