Study on Geometric Analysis

几何分析研究

• 批准号: 06452006
• 负责人: SUNADA Toshikazu
• 金额: $ 3.97万
• 依托单位: TOHOKU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06452006/
• 关键词: Global Analysis; Eigonvalue Problem; Quantum Ergodiuty; Oyerator Algebras; 幾何解析; スペクトル幾何学; エルゴード理論

1. We have found a new formulation of quantum ergodicity, and established a remarkable relationship between quantum erogodicity and classical ergodicity. A key concepts is the space average and time average in quantum mechnical systems. The method we took up is geometric analysis of pseudo differential operators and Fourier integral operators.2. We could establish a theorem on the structure of the spectrum of discrete periodic magnetic Schroedinger operators. In particular, we found a mechanism in terms of group algebras why the band structure comes out. The second cohomology group of graph-automorphism group plays an important role. It is still interesting to investigate the relation between the spectral structure and operator algebras associated with Schroedinger operators on a graph.

1. 我们找到了量子遍历性的新表述，并在量子遍历性和经典遍历性之间建立了显着的关系。一个关键概念是量子力学系统中的空间平均和时间平均。采用的方法是伪微分算子和傅里叶积分算子的几何分析。 2．我们可以建立一个关于离散周期磁薛定谔算子谱结构的定理。特别是，我们在群代数方面发现了能带结构出现的机制。图自同构群的第二上同调群起着重要的作用。在图上研究与薛定谔算子相关的谱结构和算子代数之间的关系仍然很有趣。

项目成果

板東重稔: "Stable sheaves and Eastern-Hermitian metrics" Proc. in "Geometry and Analysis on mamfdds complex. 39-50 (1994)

Shigetoshi Bando：“稳定滑轮和东埃尔米特度量”Proc.“Mamfdds 复合体的几何与分析”。39-50 (1994)

S.Bando: "Stable sheaves and Einstem-Hermitinn metrics" Proc. in Geometry and Anolgsis on complex Manifolds. 39-50 (1994)

S.Bando：“稳定滑轮和 Einstem-Hermitinn 度量”Proc。

中島 啓: "Homology of moduli spaces of instantons on ALE spaces (I)" Journal of Differential Gecmetlr. 40. 105-127 (1994)

Kei Nakajima：“ALE 空间上瞬时子模空间的同调 (I)”《微分 Gecmetlr》杂志 40. 105-127 (1994)

砂田利一: "Euclidean uersris niu-Euclideam aspectv in spectrclyeomety" Progress in Theoreticul Phys,Supplemeut. 116. 235-250 (1994)

Toshikazu Sunada：“光谱学中的欧几里得 uersris niu-Euclideamspectv”理论物理学进展，补充材料 116. 235-250 (1994)

西川青季: "Harmonic maps of unbouuded couvex polyhedvu in hypesdoli spdces" Inventioue,Mathematicae. 115. 391-404 (1994)

Aoki Nishikawa：“hypesdoli spdces 中的 unbouuded couvex polyhedvu 的调和图”Inventioue，Mathematicae 115. 391-404 (1994)