THE RESARCH OF PERATORS ON FUNCTION SPACES BY THE METHOD TO HARMONIC ANALYSIS AND RELATED ANALYSIS

调和分析法对功能空间算子的研究及相关分析

• 批准号: 14540150
• 负责人: SATO Eiji
• 金额: $ 2.11万
• 依托单位: YAMAGATA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540150/
• 关键词: Lorentz space; Hankel transform; k-hyponormal operators; deficiency; commutator; Juia set; probability densety function; Mobious transformation; 等長写像; 有理形写像; モリー空間; カオス力学系; フーリエ交換; 等長作用素; ネバリンナ理論; カオスカ学系; Lorentz space; Hankel transform; k-hyponormal operators; deficiency; commutator; Juia set; probability densety function; Mobious transformation; 等長写像; 有理形写像; モリー空間; カオス力学系; フーリエ交換; 等長作用素; ネバリンナ理論; カオスカ学系

Our purpose of this research is to study the properties of operators on function spaces by the method of harmonic analysis and related analysis. Our investigators did the research at each special point. The content is as follows:Sato studied the generalization of the relation between some operators of Hankel transforms on the positive numbers and the operators of Jacobi orthogonal system on (0,\pi). Okayasu investigated the structure of isometries on a function space and the Korovkin type linear approximation of them by contractions. Besides, he investigated the maximum part of a tuple of operators on a Hilbert space for which an indicated operator inequality holds. Mori researched about a problem of constructions of algebraically nondegenerate meromorphic mappings f of complex spaces C^m into complex projective spaces P^n(C) that for any given hypersurface D in P^n(C), f has the prescribed deficient value for D. Mizuhra showed the weak factorization theorem of H^1-functions due to Morrey functions, blocks and the Riesz potential. Also applying this result, we observed the necessity for which the commutator between the Riesz potential and a locally integrable function to be bounded on Morrey Spaces. Nakada studied some geometric properties of the Julia set of rational functions on the Riemann sphere. In particular, it is concerned with the group of euclidean motions which keep invariant the Julia set. Kawamura discussed an generalization of the theory concerning the behavior of probability density functions associated with chaotic maps on a measure space. The spaces he considered were AL and AM spaces and he generalized a convergence theory of probability density functions. Sekigawa examined some examples of transformations with torsion acting on the 3-dimensional Euclidean space by using Clifford matrix representations of M\" obius transformation.

这项研究的目的是通过谐波分析和相关分析的方法研究操作员在功能空间上的特性。我们的调查人员在每个特殊点进行了研究。内容如下：SATO研究了汉克尔（Hankel）某些操作员对正数的概括与雅各比正交系统的运算符（0，\ pi）上的运算符之间的关系。 Okeasu调查了功能空间上的异构体的结构，并通过收缩对它们的Korovkin型线性近似。此外，他调查了运营商元组的最大部分，在希尔伯特空间中，指示的操作员不平等所持有的最大部分。莫里（Mori）研究了复杂空间中代数非排定的杂物映射f的构建问题，以c^m的c^m c^n（c）中的任何给定的高表情D（c）中的任何给定的超表面d，f在p^n（c）中，f具有D. mizuhra的规定不足值，d。mizuhra均表明了h^1-frimanials的弱点和较弱的均值。同样在应用此结果时，我们观察到了Riesz电位与局部积分函数之间的换向器的必要性，该函数要限制在Morrey空间上。 Nakada研究了Riemann Sphere上朱莉娅（Julia）合理函数集的一些几何特性。特别是，它关注的是欧几里得运动的群体，这些动议使朱莉娅设定不变。川村讨论了有关与混乱图在测量空间上与混沌图相关的概率密度函数行为的理论的概括。他认为的空间是Al和AM空间，他概括了概率密度函数的收敛理论。 Sekigawa通过使用M \“ Obius Transformation的Clifford Matrix表示，扭转作用在三维欧几里得空间上的转化示例。