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研究了H^*上复合算子的分支问题，得到了与IL赵教授几乎一致的答案。我们在1998年柏林加尔马利国际艺术博览会的海报会议上进行了一次交谈。演讲结束后，WC将结果汇总到与贝塔教授的一篇论文中)。麦奇尔和(L)提交。此外，Olino还研究了一些超范函数空间、圆盘代数、H^*和Bloch空间上的加权复合算子。和R.Zha.o在小Bloch空间的情况下增加了结果。Funabashmi研究了SP(1)轨道的时间几何性质，这些轨道是通过对Kachler 6球面时间的特殊类型的三种作用来实现的。我们证明了每个轨道都是一个流形，并且One轨道装备了具有三个不同主曲率的接触CR-结构。这些成果将在不久的将来做出贡献。我们还研究了…中的接触CR子流形更多的萨萨克空间形态。我们的主要结果是，一些完全接触的Al-脐接触CR子流形被实现为浸入三维球面的二维环面。为了得到这些结果，我们将与S.Funabashi，J.H.Kuan和J.S.Pak合作撰写题为《关于完全接触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用纯粹虚构的Octon ion IMO(或Cayley代数)标识了7维欧几里德空间。考虑到八元数的代数性质，我们可以定义S^6上的齐次几乎伊特结构，我们用G_2表示O的自正交的李群，然后我们有S^6=G_2/SU(3)。这个准colnj)lex结构满足近Kahler条件。((*XJ)X=0)其中*是S^6的Levi-Civita联络，X是S^6的任意向量场。我们将给出G_2作用下的一些不变子流形的刚性定理，从而确定G_2的几何不变量。此外，我们还将给出S^6的三维CR-SNB流形的许多例子。我们得到了与S^6的四维CR子流形有关的一些结果。(4)石崎一郎研究了亚纯函数的值分布理论。将这一理论应用于复杂的NP个十六进制微分方程组是我们感兴趣的。考虑了允许解的代数微分方程解和复振动理论。我们还讨论了复平面上的函数方程。得到了Schmrdder型泛函方程超越亚纯解的存在性和增长性条件，这些结果是Wittich的推广。此外，我们还研究了一类泛函方程亚纯解的超超越性。亚纯集合的刻划。(5)ETO研究了么半环，特别是仿射半群环的同伦性质。为了做到这一点，在两种情况下，我结合地构造了它们的自由分解。它们见于“二项式理想的自由解”和“非正则环的有限自由解”两篇文章。较少

项目成果

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.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.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）。