Studies of The Spaces of Analytic Functions and Their Operators

解析函数空间及其算子的研究

基本信息

批准号：
07640242
负责人：
OHNO Shuichi
金额：
$ 1.41万
依托单位：
Nippon Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640242/
关键词：
Hardy Space Tociplitz Operator Composition Operator Manifold Grassmann Geometry Sphere Differential Equation Entire Function angular derivative 多様体グラスマン幾何 Bergman空間 Hapf超曲面リーマン面整関数

项目摘要

(1) In 1995, Ohno investigated Toeplitz and Hankel operators on harmonic Borgman spaces on the unit disk. Main results are to characterize algebraic properties, boundedness and compactness. There exists a relation between the compactness of Hankel operators and Bourgain algebras. This is a very interesting problem. In 1996, he studied the conditions that differences of two composition operators are compact. He obtained some examples and a necessary condition closely related to the compactness of one composition operator.(2) Funabashi studied 5-dimensional submanifolds of a nearly Kaehler 6-spherc in the purcly imaginary octonians. Main result is that for any hypersurface of 6-sphere, there exists a grobal quaternion structure on the contact distribution. Moreover he studied tublar hypersurfaces. He iedentified the symplectic group SP (1) with the 3-dimensional sphere and considered parametrized 3-dimcnsional submanifolds in terms of SP (1) -orbits in the 6-sphere.(3) Hashimoto investig … More ated submanifolds theory in a 6-dimensional sphere S^6. A 6-dimensional sphere has an almost Hermitian structure.It was proved that n-dimensional sphere admit almost complex structures except for n*2,6. Also the automorphism group of this almost Hcrmitian structure of S^6 coincide with the exceptional Lie group G_2. The 2-dimensional submanifolds of a 6-dimensional sphere is called the J-holomorphic curves of S^6 if its tangent space is invariant under the almost complex structure. I obtained some classification theorems and a rigidity theorem with respect to the Lie group G_2 about J-holomorphic curves of S^6.(4) Ishizaki has studied the complex differential equations, mainly admissible solutions of first order algebraic differential equations and complex oscillation for an equation of the form f"+A (z) f=0. Complex dynamics theory has been also of our great interest. Study of hypertranscendency has treated from the two points of view, say complex differential theory and complex dynamics theory. Less

（1）1995年，OHNO在单位磁盘上的谐波Borgman空间上调查了Toeplitz和Hankel运营商。主要结果是表征代数特性，有限性和紧凑性。 Hankel操作员的紧凑性与天桥代数之间存在关系。这是一个非常有趣的问题。 1996年，他研究了两个组成算子的差异紧凑的条件。他获得了一些例子和与一个组成算子的紧凑性密切相关的必要条件。（2）在纯粹想象中的octonians中，Funabashi研究了几乎kaehler 6-Sphere的funabashi 5维次符号。主要结果是，对于6个距离的任何超表面，触点分布上都存在全球季节结构。此外，他研究了管状高度曲面。他用3维球体将符号组SP（1）授予了sp（1） - hashimoto研究中的sp（1）孔。一个6维的球体几乎具有荒凉的结构。证明N维球几乎接受了n*2,6以外的几乎复杂的结构。这也是S^6的几乎hcrmitian结构的自动形态组与特殊的Lie组G_2一致。如果其切线空间在几乎复杂的结构下是不变的，则6维球的二维亚策略称为S^6的J旋晶曲线。我获得了一些分类定理和关于谎言组的G_2的分类定理，涉及s^6的J-丝晶曲线。（4）Ishizaki研究了复杂的微分方程，主要是一阶代数代数差分方程的一阶方程和复杂振动的一阶代数方程的解决方案，以及对f”（Z）的较为f = 0。从两种观点（复杂的差异理论和复杂的动力学理论）从两种观点开始处理