Studies of The Structures of Analytic Function Spaces and Their Operators

解析函数空间及其算子的结构研究

• 批准号: 09640218
• 负责人: OHNO Shuichi
• 金额: $ 1.98万
• 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: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640218/
• 关键词: Hardy Space; Composition Operator; Hopf hypersurface; Cayley algebra; Automorphism group; Meromorphic function; Complex functional equation; Monoid rings; 超越函数; スピノール群; 値分布論; 自由分解

(1) Ohno has investigatcd the 1)robleln of components of composition operators on H^* and obtained almost conIl)Iete answers with Professor IL Zhao. We had a talk at Poster Session in International Matlnnaticiazhs Goiigrcss 1998, Berlin, Garmany. After thc talk, wc summarized results to a paper with Profcssor beta.D). MacChicr and(l submitted it. Moreover Olino have studied weighted composition operators on some sup-norm function spaces, the disk algebra, H^* and the Bloch space. And R.Zha.o added results in the case of the case little Bloch space. We are ready to submit a manuscript.(2) Funabashmi studied time geometrical properties of the SP(1)-orbits which are realized by the special kinds of three actions to tIme nearly Kachler 6-sphere. We proved that each orbit is a manifold and somne orbit equips the contact CR-structure having the three distinct principal curvatures. Those results will be contributed in the imear future. We also studied about contact CR-submanifolds immersed in … More Sasakian space forms. Our maun results is that some totally contact Al-umbilical contact CR-submanifold is realized as the 2-dimensional torus immersed in the 3-dimensional sphere. For those results, we will contribute the paper entitled "On totally contact Al-umbilical contact CR-submanifolds" in collaboration with S.Funabashi, J.H.Kwon and J.S.Pak.(3) Let S^6 be the 6-dimensional unit sphere centered at the origin in a 7-dimensional Euclidean space. Hashimnoto identified 7-dimensional Euchidean space with purely imaginary octon ions ImO (or Cayley algebra). Taking account of algebraic properties of octonions we can define the homogeneous almost Itermitian structure on S^6, We denote by G_2 the Lie group of autornorphisms of O.Then we have S^6 = G_2/SU(3). This almost colnj)lex structure satisfy the nearly Kahler condition. ((*xJ)X = 0) where * is the Levi-Civita connection of S^6, and X is any vector field of S^6. We shall give some rigidity theorem of invariant submanifolds up to the action of G_2 amid deterirmine its geometrical invariants. Also, we shall give many examples of 3-dimensional CR-snbmanifolds of S^6 explicitely. We obtained some results related to 4-dimensional CR-submanifolds of S^6.(4) Ishmizaki has beemi studying the value distribution theory of meromorphic functions. Applications this theory to com np hex differential equations are of our interest. Algebraic differential equations admitting admissible solutiomis and complex oscillation theory have been comisidered. We are also concerned with functional equations in the complex plane. Results of existence and growth conditions on transcendental meromorphic solutions of Schmrdder's type functional equations, which are some generalizations due to Wittich, are obtained. Moreover, we investigated to lmypertranscendency of merornorphic solutiohs of a certain functional equation. Characterization of the set of meromorphic. functions has been studied from the unicity tlmeoretical poimits of view.(5) Eto investigated homnological properties of monoid rings, especially affine semigroup rings. To do it, lie comistructedI free resolntiomis of them in two cases conibinatorically. They are found in papers "a free resolutions of a binomial ideal" and "finite free resolutions of rnonoid rings". Less

(1)Ohno在H^* 上证明了复合算子分支的问题，并得到了与赵一龙教授几乎一致的答案。我们在1998年柏林加玛尼国际展览会海报会议上进行了交谈。演讲结束后，我们将结果总结成一篇论文。MacChicr和（l）提出的，Olino还研究了一些超范数函数空间、圆盘代数、H^* 和Bloch空间上的加权复合算子。并在小Bloch空间的情况下，推广了R.Zha.o的结果.我们已经准备好提交手稿。(2)Funabashmi研究了由三种特殊的作用量实现的SP（1）-轨道的时间几何性质。我们证明了每个轨道都是流形，并且每个轨道都具有三个不同主曲率的接触CR结构。这些结果将在不久的将来提供。我们还研究了浸入的切触CR子流形 ...更多信息 Sasakian空间形式我们的马翁结果是：某个全切触Al-脐切触CR-子流形被实现为浸入三维球面中的二维环面。对于这些结果，我们将与S.船桥，J.H.Kwon和J. S. Pak合作，贡献题为“关于全接触Al脐接触CR子流形”的论文。(3)设S^6是7维欧氏空间中以原点为中心的6维单位球面。Hashimnoto确定了7维Euchidean空间与纯虚八子离子ImO（或凯莱代数）。考虑到八元数的代数性质，我们可以定义S^6上的齐次几乎迭代结构，用G_2表示O的自同构李群，则有S^6 = G_2/SU（3）。这种近似列结构满足近似Kahler条件。（（*xJ）X = 0）其中 * 是S^6的列维-奇维塔联络，X是S^6的任意向量场。在证明G_2的几何不变量的同时，给出了G_2作用下不变子流形的刚性定理。此外，我们还将明确地给出S^6的三维CR-流形的许多例子。我们得到了一些与S^6的四维CR-子流形有关的结果。(4)Ishmizaki一直致力于研究亚纯函数的值分布理论。应用这一理论的COM NP十六进制微分方程是我们的兴趣。讨论了容许解的代数微分方程和复振动理论。我们也关心复平面上的函数方程。得到了Schmrdder型函数方程超越亚纯解的存在性和增长性条件，推广了Wittich的结果。此外，我们还研究了一类函数方程亚纯解的超超越性。亚纯函数集的特征。从统一性的观点出发，对函数进行了研究。(5)埃托研究了幺半群环，特别是仿射半群环的同调性质。为此，在两种情况下，联合使用了两种方法。他们发现在文件“一个自由决议的二项式理想”和“有限自由决议的rnonoid环”。少

项目成果

K.Ishizaki(共): "Unicity theorems for meromorphic sharing four small functions" Koclai Muth. J.21. 350-371 (1998)

K.Ishizaki(co)：“亚纯共享四个小函数的唯一性定理”Koclai Muth J.21 (1998)。

S.Ohno: "Rocky Mountain Mathematis Consortium Summer Conference 1996 Composition Operators on spaces of analytic functins" Report of Reseanches N.I.T. 26. 421-436 (1997)

S.Ohno：“落基山数学联盟夏季会议 1996 年分析函数空间的组合算子”N.I.T 研究报告

K.Eto: "Cohen-Macaulay rings associated with digraphs" J.Algebra. 206. 541-544 (1998)

K.Eto：“与有向图相关的科恩-麦考利环”J.代数。

K.Izuchi(共): "Self adjoint commutators and invariant subapaces on the tows II" Integral Eguations and Operator Theory. 27. 208-220 (1997)

K. Izuchi（合著者）：“丝束 II 上的自伴随交换子和不变子空间”积分方程和算子理论 27. 208-220 (1997)。

T.Koda(共): "Grasamann Geometry of 6-dimensional sphere" Topics in Complex Aralysis,Differential geometry and mathematical Physics. (1997)

T.Koda（合作）：“六维球体的格拉萨曼几何”复数分析、微分几何和数学物理主题（1997）。