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Theory and application of Fourier analysis

傅立叶分析理论与应用

基本信息

批准号：
12640165
负责人：
OKUYAMA Yasuo
金额：
$ 1.15万
依托单位：
SHINSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640165/
关键词：
orthogonal series absolute Norlund summability nets algebraic Riccati equation martingale-like sequences weak convergence of vector measures uniform tightness seml-Riemannian submersion 絶対リース総和法フィルター H∞制御問題 Thueの問題双線形ベクトル積分アファ

项目摘要

Some of our important research results are as follows:1. We established a general theorem on the generalized absolute Norlund summability of orthogonal series which contains some theorems on the absolute Norlund summability and the Riesz suinmability of orthogonal series.2. We studied carefully about equivalence of the convergence of filters on a topological space and the convergence of nets in the space, ffe summarized the equivalence transparently as it is convenient in arguments in analysis.3. The point of solvability for H∞ control problems is the existence of a non-negative definite solution to the associated algebraic Riccati equation. The uniqueness of the above solution is proved for general plants in both continuous-time and discrete-time systems.4. The two convergence theorems of martingales in the limit, i. e. L1-boundedness and integrability of stopped process, are compared, and it is found that the earlier would imply the late. We gave a proof that some sequence of letters … More is qubic-free.5. A type of Strassen's theorem for the existence of probability measures with given marginals is extended to positive vector measures with values in the dual of a barred locally convex space which has certain order conditions.6. By an essential use of the Bartle bilinear integration, it is shown that the injective tensorproduct of positive vector measures in certain Banach lattices, is jointly continuous with respect to the weak convergence of vector measures.7. We discuss the semi-Riemannian submersion with affine connection and seek its fundamental equations. We define the another almost complex structure ( resp. almost contact structure ) and an indefinite Kahlerian ( resp. Sasakian) manifold with affine connection, moreover we consider the case which the total space admits these structures.8. We study on the Riemannian submersionwith α-connection, We show that if the total space is of an n-dimensional normal distribution, then the base space is of positive definite symmetric matrices of order n, the horizontal distribution is integrable and each fiber is α-flat. Also, we discuss geodesic equations on the statistical model of the multinariate normal distribution. Less

主要研究成果如下：1.建立了正交级数广义绝对Norlund可和性的一个一般定理，其中包含了正交级数绝对Norlund可和性和Riesz可和性的一些定理.我们仔细研究了拓扑空间上滤子收敛与拓扑空间中网收敛的等价性，ffe对这一等价性进行了透明的总结，便于分析论证. H∞控制问题的可解性的关键是其代数Riccati方程的非负定解的存在性。对于一般对象，证明了上述解在连续时间和离散时间系统中的唯一性.给出了极限鞅的两个收敛定理，即极限鞅的收敛定理. e. L1-有界性和停止过程的可积性进行了比较，发现停止过程的L1-有界性越早，可积性越晚。我们证明了一些字母序列 ...更多信息是qubic-free的。将一类关于具有给定边缘的概率测度存在性的斯特拉森定理推广到值在具有一定序条件的禁止局部凸空间的对偶中的正向量测度.通过Bartle双线性积分的重要应用，证明了某些Banach格中正向量测度的内射张量积关于向量测度的弱收敛是联合连续的。7.讨论了仿射联络的半黎曼浸入，并求出了它的基本方程。我们定义了另一个几乎复杂的结构（分别为）。几乎接触结构）和不定Kahlerian（分别。Sasakian）流形，并且考虑了全空间允许这些结构的情况.本文研究了具有α-联络的黎曼浸没问题，证明了若全空间为n维正态分布，则基空间为n阶正定对称矩阵，水平分布可积，且每根纤维是α-平坦的.并讨论了多元正态分布统计模型的测地线方程。少