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Cooperative Researches on Real Analysis and Functional Analysis

实分析与泛函分析的合作研究

基本信息

批准号：
01302004
负责人：
SAKATA Hiroshi
金额：
$ 8.96万
依托单位：
Okayama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1989
资助国家：
日本
起止时间：
1989 至 1990
项目状态：
已结题

项目摘要

1. In the area of real analysis, various results pertaining to harmonic analysis on Euclidean domains were obtained. Among others, a theory of H^P space was developed in detail. A new development of Harmonic analysis was established. The latter was deeply related to differential geometry, partial differential equations and stochastic processes.2. In the area of applications of function spaces, new aspects of quantum information theory were obtained and applied to irreversible processes. Matrix inequalities in multiport network connections were studied. Various results in the field of evolution equations were obtained and applied to partial differential equations.3. In the area of representation theory and harmonic analysis, remarkable results were obtained. Discontinuous group in a homogeneous space of reductive type was studied. A construction of infinite-dimensional Lie groups was realized. Invariance of dimension of solutions to homogeneous characteristi cequations on semisimple Lie groups was clarified.4. In the area of functional analysis and partial differential equations, evolution equations, pseudo-differential operators, nonlinear parabolic equations, inverse eigenvalue problems, evolution equations in Hilbert spaces, hyperfunctions and Schrodinger equations were successfully developed.5. In the area of operator algebras and function algebras, the theory of unbounded derivations in C^*-algebras was developed and applied to statistical mechanics. Structure of operator algebras, quantum groups, structure of unbounded operator algebras, and function algebras were analyzed in detail.

1.在实分析领域，获得了欧几里德域上调和分析的各种结果。其中，详细发展了 H^P 空间理论。建立了谐波分析的新发展。后者与微分几何、偏微分方程和随机过程密切相关。 2．在函数空间的应用领域，获得了量子信息论的新方面并将其应用于不可逆过程。研究了多端口网络连接中的矩阵不等式。得到了演化方程领域的各种成果，并将其应用于偏微分方程中。 3．在表示论和调和分析领域取得了显著成果。研究了还原型齐次空间中的不连续群。实现了无限维李群的构造。阐明了半单李群上齐次特征方程解的维数不变性。 4．在泛函分析和偏微分方程领域，成功发展了演化方程、伪微分算子、非线性抛物型方程、反特征值问题、希尔伯特空间演化方程、超函数和薛定谔方程等。 5．在算子代数和函数代数领域，C^*-代数的无界导数理论得到发展并应用于统计力学。详细分析了算子代数的结构、量子群、无界算子代数的结构、函数代数。