Harmonic Analysis on Symmetric Spaces

对称空间的调和分析

基本信息

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

项目摘要

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。在这个项目下，奥岛（Oshima）于1988年1月在东京大学组织了一个症状，并于1988年8月和1989年8月在职业培训研究所举行了夏季精灵，我们讨论了该项目的当前阶段及其未来的发展。2。 Oshima发表了一些重要的结果，这些结果将用于在半精密对称空间（Plancherel公式）上获得谐波分析的主要目的。它们如下：Oshima在紧凑的歧管中意识到对称空间的平稳嵌入，并且通过使用它，Oshima为不变差分算子的特征函数构建了边界值图，并发现无穷大的特征函数的不对称是由简单的几何形状结构表征的。通过相同的方法，奥希马证明了在均匀空间上实现的可单位化的Harish-Chandra模块的一定界限3。 Kobayashi在同质空间上计算了Laplacian的光谱，该空间是Riemann上的纤维束……更多的Ian对称空间。这给出了Sunada提出的猜想的反面例子。 Kobayashi还证明了在几个半密布对称空间中存在统一晶格。4。 Hattori为在歧管的尺寸很小时，在几乎复杂的歧管上为线束提供了某种消失的Kodaira类型理论。5。 Masuda显示了Gierer-Meinhard作为生物形成的数学模型的某些反应扩散系统的溶液的存在和界限。6。伊哈拉（Ihara）研究了绝对的加洛伊斯（Galois）小组，及其在某个代数歧管的基本组完成的自然行动中及其自然行动。伊哈拉（Ihara）明确指出，这些行动给出了加洛伊斯（Galois）组的足够一般的非亚伯利亚代表，并获得了数字理论的几种应用。7。 Kataoka和Tose扩展了由Sjostrand源自Sjostrand的微局部双曲线边界值问题的规律性的微局部传播理论。他们的结果还包含解决方案的理论。较少的