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

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.

本文的研究目的是用调和分析和相关分析的方法研究函数空间上算子的性质。我们的调查人员在每个特殊的地点都做了调查。内容如下：Sato研究了正数上的一些Hankel变换算子与（0,\pi）上的Jacobi正交系统算子之间关系的推广。Okayasu研究了函数空间上的等距结构以及它们的Korovkin型线性逼近。此外，他还研究了希尔伯特空间上存在一个指示算子不等式的算子元组的极大部分。Mori研究了复空间C^m的代数非退化亚纯映射f到复射影空间P^n(C)的构造问题，即对于P^n(C)中任意给定的超曲面D， f对D具有规定的亏缺值。Mizuhra由于Morrey函数、块和Riesz势，给出了H^1函数的弱分解定理。同样应用这一结果，我们观察到Riesz势与局部可积函数之间的对易子在Morrey空间上有界的必要性。Nakada研究了黎曼球上有理函数Julia集的一些几何性质。特别地，它关注保持Julia集合不变的欧几里得运动群。Kawamura讨论了关于混沌映射在测量空间上的概率密度函数行为的理论的推广。他考虑的空间是AL和AM空间，并推广了概率密度函数的收敛理论。Sekigawa用M\ obius变换的Clifford矩阵表示检验了一些具有扭转作用于三维欧几里得空间的变换的例子。

项目成果

Y.Komori, T.Mizuhara: "Notes on Commutators and Morrey spaces"Hokkaido Math.J.. VOl.32. 345-353 (2003)

Y.Komori，T.Mizuhara：“关于换向器和莫雷空间的注释”Hokkaido Math.J.. VOl.32。

E.Sato: "Lorentz multipliers for Hankel transforms"Science mathematicae Japonicae. Vol.59,No.3(to appear).

E.Sato：“汉克尔变换的洛伦兹乘子”日本数学科学。

T.Okayasu, T.Hachiro: "Some theorems of Korovkin type"Studia Math.. 155(2). 131-143 (2003)

T.Okayasu、T.Hachiro：“Korovkin 型的一些定理”Studia Math.. 155(2)。

S.Mori: "Meromorphic mappings and deficiencies"Advanced Studies in Pure Math., Complex Analysis is Several Variables.

S.Mori：“亚态映射和缺陷”纯数学高级研究，复分析是多个变量。

Y.komori: "Notes on commutators and Morrey spaces"Hokkaido Math.J.. 32. 345-353 (2003)

Y.komori：“关于交换子和莫雷空间的注释”Hokkaido Math.J.. 32. 345-353 (2003)