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Research on Applications of Real and Functional Analysis

实数分析和泛函分析的应用研究

基本信息

批准号：
60302005
负责人：
MURAMATU Tosinobu
金额：
$ 7.42万
依托单位：
University of TSUKUBA
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1985
资助国家：
日本
起止时间：
1985 至 1986
项目状态：
已结题

项目摘要

We investigated various fields in real analysis and functional analysis, and have obtained many results which are closely related to partial differential equations, mathematical physics, probability theory and differential geometry. Some of important results are as follows.1. Application to Partial Differential Equations.Nonlinear Schrodinger equation, Vlasov-Maxwell equation, some nonlinear eigenvalue problems, precise sufficient conditions for boundenness of pseudo-differential operators, differential operators of infinite order general boundary value problems in the framework of hyperfunctions, 2nd microlocalization.2. Operator Algebra.Jones' index of factor algebra, investigation on Baum-Connes conjecture functional calculus for Banach function algebra, Hardy spaces of 2-parameter Brownian martingales.3. Function Spaces.Douglas algebra and inner functions, domain of Parreu-Widom type, convex programming on spaces of measurable functions, orthogonality in normed spaces, nonlinear evolution operators in Banach spaces and their applications to concrete problems.4. Real Analysis.Fourier transform for functions of several variables, singular integral operators, harmonic analysis on groups, harmonic anslysis on manifolds of negative curvature.5. Representation of Lie Groups.Semi-simple groups, Semi-simple symmetric spaces, Fourier transform on symmetric spaces, monomial representations of solvable group, theory of D-modules, applications of representation of infinite dimentional groups to physics.

我们研究了真实的分析和泛函分析的各个领域，得到了许多与偏微分方程、数学物理、概率论和微分几何密切相关的结果。主要结果如下：1.应用于偏微分方程，非线性薛定谔方程，Vlasov-Maxwell方程，一些非线性特征值问题，伪微分算子有界性的精确充分条件，超函数框架下无穷阶一般边值问题的微分算子，第二微局部化.算子代数，因子代数的Jones指标，Banach函数代数的Baum-Connes猜想泛函微积分研究，二指标布朗鞅的哈代空间.函数空间、道格拉斯代数与内函数、Parreu-Widom型域、可测函数空间上的凸规划、赋范空间中的正交性、Banach空间中的非线性演化算子及其在具体问题中的应用.真实的分析.多元函数的傅里叶变换，奇异积分算子，群上的调和分析，负曲率流形上的调和分析.李群的表示。半单群，半单对称空间，对称空间上的傅立叶变换，可解群的单项式表示，D-模理论，无限维群的表示在物理学中的应用。