Studies of The Spaces of Analytic Functions and Their Operators

解析函数空间及其算子的研究

• 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

(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研究了单位圆盘上调和Borgman空间上的Toeplitz和Hankel算子。主要结果是刻画代数性质、有界性和紧性。Hankel算子的紧性与Bourgain代数之间存在着某种联系。这是一个非常有趣的问题。1996年，他研究了两个复合算子的差是紧的条件。他得到了一些例子和一个必要条件密切相关的紧凑性的一个组成运营商。(2)船桥研究了纯虚八元数中的近Kaehler 6-球面的5维子流形。主要结果是：对于任意6-球面超曲面，其切触分布存在球四元数结构。此外，他研究tublar超曲面。他用3维球面定义了辛群SP（1），并考虑了用SP（1）-轨道表示的参数化3维子流形。(3)桥本调查 ...更多信息 6维球面中的对称子流形理论[S^6]。证明了6维球面具有几乎厄米特结构，而n维球面除了n* 2，6外，几乎具有复结构。而且，S^6的这种几乎赫米特结构的自同构群与例外李群G_2重合。一个6维球面的2维子流形称为S^6的J-全纯曲线，如果它的切空间在几乎复结构下是不变的。得到了关于S^6的J-全纯曲线的李群G_2的一些分类定理和一个刚性定理。(4)石崎研究了复微分方程，主要是一阶代数微分方程的容许解和形式为f”+A（z）f=0的方程的复振动。复杂动力学理论也引起了我们极大的兴趣。超超越的研究主要从复微分理论和复动力学理论两个角度进行。少

项目成果

H.Hashimoto(共): "Hypersurfaces in a 6-dimensional sphere" J.of karean Math Soc. (近刊).

H.Hashimoto（合著者）：“六维球体中的超曲面”J.of karean Math Soc（即将出版）。

K,Ishizaki(共): "On admissible solutions of algebraic differential equations" Funkcialaj Ekvacioj. 38. 433-442 (1995)

K, Ishizaki (co)：“关于代数微分方程的容许解”Funkcialaj Ekvacioj 38. 433-442 (1995)。

K.Ishizaki and K.Tohge: "On the comlex oscilltion of some linear differential equations" J.Math.Anal.Appl.(to appear).

K.Ishizaki 和 K.Tohge：“关于某些线性微分方程的复杂振荡”J.Math.Anal.Appl.（即将出现）。

Hideya Hashimoto: "Minimal surfaces in a 4-dimensional sphere" Houston Math. J.21. 449-463 (1995)

Hideya Hashimoto：“4 维球体中的最小曲面”休斯顿数学。

K.Ishizaki(共): "On the complex oscillation of some linear differential equations" J,Math.Anal Appl. (近刊).

K. Ishizaki（合著者）：“关于某些线性微分方程的复振荡”J，Math.Anal Appl（即将出版）。