Theory and application of Fourier analysis

傅立叶分析理论与应用

• 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

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

我们的一些重要研究结果如下：1。我们建立了一个关于正交系列的普遍诺伦总和的一般理论，其中包含一些关于绝对诺伦的总结性和正交系列的riesz suinmity.2。我们仔细研究了过滤器在拓扑空间和空间中网的收敛性上的等效性，FFE在分析中的参数中方便地透明地汇总了等效性。3。 H∞控制问题的可溶性点是存在针对相关代数riccati方程的非负定溶液。在连续时间和离散时间系统中，通用植物证明了上述解决方案的独特性。4。比较了Martingales的两个融合定理，即比较L1结合和停止过程的整合，发现越早暗示较晚的时间。我们给出了一些字母序列……更多是无量子的。5。具有给定边缘的概率测量的一种类型的strassen定理扩展到正向矢量测量值，其值是具有某些阶端条件的局部凸空间的双重值。6。通过对Bartle双线性整合的必要用途，可以表明，对于某些Banach晶格中阳性矢量测量的射量张力，与矢量测量的弱收敛性相对于7。我们讨论了具有仿射连接的半帝国浸没，并寻求其基本方程式。我们定义了另一个几乎复杂的结构（分别是接触结构）和具有仿射连接的无限kahlerian（分别为sasakian）歧管，此外，我们考虑了总空间允许这些结构的情况。8。我们研究了带有α-连接的里曼尼亚浸没，我们表明，如果总空间为n维正态分布，那么基本空间是n阶的正面定义的对称物质，则水平分布是可集成的，每个纤维都是α-flat。此外，我们讨论了多种正态分布的统计模型上的大地测量方程。较少的

项目成果

Kawabe,J.: "Joint continuity of injective tensor products of vector measures in Banach lattices"Austral. Math. J. Ser. A. ( to appear ).

Kawabe，J.：“Banach 晶格中向量测度的单射张量积的联合连续性”Austral。

河邊 淳: "Uniform tightness for transition probability on a nuclear space"京都大学数理解析研究所講究録. (印刷中).

Jun Kawabe：“核空间上转移概率的均匀紧密性”Kokyuroku，京都大学数学科学研究所（正在出版）。

Jun Kawabe: "Compactness and metrizability in the space of vector measures in locally convex spaces"Sci. Math. Japonicae. (印刷中).

Jun Kawabe：“局部凸空间中向量测度空间的紧致性和可度量性”Sci。

Takashi Mitsuishi: "Fuzzy optimal control using simple inference method and function type inference method"Proc. Amer. Control Conf.. 1944-1948 (2000)

Takashi Mitsuishi：“使用简单推理方法和函数类型推理方法的模糊最优控制”Proc。

Takashi Mitsuishi: "Optimization of fuzzy feedback control L∞ space"Proc 10th IEEE Intern. Conf. Fuzzy Systems. (印刷中).

Takashi Mitsuishi：“模糊反馈控制 L∞ 空间的优化”Proc 10th IEEE 模糊系统（正在出版）。