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

基本信息

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

项目摘要

(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对1）构成操作员组成的Roblen进行了研究，并与Il Zhao教授获得了几乎Conil的答案。我们在国际Matlnnaticiazhs Goiigrcss 1998年，柏林，Garmany举行了一场演讲。 THC讨论后，WC将结果汇总到Profcssor beta.d的论文中。 MacChicr和（l提交了。此外，Olino在某些Sup-Norm功能空间，磁盘代数，H^*和Bloch空间和R.Zha.O中添加了加权组成操作员。和R.Zha.o在情况下增加了结果。在几乎是kachler的三个动作中，我们证明了每个轨道是一种跨度的轨道，与三个不同的主体曲线相当。二维圆环浸入了三维领域，我们将与S.Funabashi，J.H.Kwon和J.S.-Pak合作，为“完全接触Al-bumbilical接触CR CR-SUBMANIFOLDS”贡献，该论文是6维单元的SPRAPINE（3）。 Hashimnoto鉴定了具有纯粹想象的八个离子IMO（或Cayley代数）的7维辉体空间。考虑到八元的代数特性，我们可以在s^6上定义几乎均匀的结构，我们用g_2表示O的lie of o的自构态。然后，我们有s^6 = g_2/su（3）。这种几乎colnj）的结构几乎满足了卡勒的条件。（（ * xj）x = 0）其中 *是s^6的levi-civita连接，而x是s^6的任何向量字段。我们将给出一些不变的子曼群的刚性理论，以决定其几何不变的g_2的作用。另外，我们将明确地提供许多S^6的3维Cr-SnbManifolds的例子。我们获得了一些与S^6的4维Cr-Submanifolds相关的结果。（4）Ishmizaki已经研究了Meromormorthic函数的价值分布理论。应用该理论对六角差分方程是我们感兴趣的。已提出了接受可允许的实体和复杂振荡理论的代数微分方程。我们还关注复杂平面中的功能方程。获得了Schmrdder类型功能方程的先验物质溶液的存在和生长条件的结果，这是由于Wittich引起的一些概括。此外，我们调查了某个功能方程的merormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormorormormormormormorormormormorormormormormorormormormormormormormormormormormormormormormormormormorriohs。一组Meromorthic的表征。函数已经从统一的视野统一性研究中进行了研究。（5）ETO研究了单体环的家庭学特性，尤其是仿射半群环。为此，在两种情况下，comistructedi lie comistructedi无溶剂的分解。它们在“二项式理想的自由分辨率”和“ Rnonoid环的有限的无限分辨率”中发现。较少的