QUANTITATIVE RESEARCH OF DEFICIENCIES OF MEROMORPFIC MAPPINGS AND EXCEPTIONAL MAPPINGS

亚形作图和异常作图缺陷的定量研究

• 批准号: 15540151
• 负责人: MORI Seiki
• 金额: $ 2.3万
• 依托单位: Yamagata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540151/
• 关键词: value distribution theory; meromorphic mapping; defect; unicity theorem; hypersurface; complex dynamical system; complex projective space; function space; 力学系; ジュリア集合; カオス力学系

The head investigator Mori researched a sparsity of meromorphic mappings with defects. He obtained elimination theorems of defects of hypersurfaces or rational moving targets of a meromorphic mapping into P^n(C) by a small deformation, and he also proved that mappings without defects are dense in a space of transcendental meromorphic mappings. He and an investigator Aihara also obtained results that for any hypersurface of degree d on P^n(C), we can construct an algebraically nondegenerate meromorphic mapping with a preassaigned deficiency in an interval (0,α), where α>0 depends only on d. Mori also studied on uniqueness theorems of meromorphic functions. There are many results on uniqueness sets, but it seems that there are few results on uniqueness domains. We are going to find an unbounded domain in C such that a uniqueness theorem holds under the condition restricted on the domain. Mori, Lin and Tohge gave a uniqueness theorem under the condition restricted on an angular domain, an … More d the paper was submitted. An investigator Aihara obtained several conditions on the inverse image of a divisor under meromorphic mappings for which mappings are algebraically dependent, and he also obtained a condition under which two analytic ramified covering spaces are identical. This is a geometric extension of a uniqueness theorem of algebroid functions. Nakada investigated a complex dynamics of Blachke products like rational functions, especially, an estimate of a Hausdorff dimension and the invariance of Julia set under Euclidean congruent transformation. Sekigawa investigated a limit set of a sequence of Moebius transformations acting on C, and also he treated Moebius transformations acting on a general dimension space. He also studied an expression of Moebius transformations using Cliford matrix, and its applications. Kawamura studied an orbit of probabilistic density function, and also he gave a proof of a properties of topological conjugate maps on a group of Tent maps, after computer simulation. Sato gave a generalization of relation between Jacobian orthogonal system and an operators on a function space and an operators on Hankel transformations. Mizuhara proved a weak decomposition theorem related to a function on a generalized Morrey space and Block and Calderon-Zygmund operators. Less

首席研究员Mori研究了具有缺陷的亚纯映射的稀疏性。他通过小变形得到了亚纯映射到P^n(C)上的超曲面或有理运动目标的亏空的消去定理，并证明了在超越亚纯映射空间中，没有亏空的映射是稠密的。他和研究员Aihara还得到了结论：对于P^n(C)上的任意d次超曲面，我们可以构造一个在区间(0，α)上有预缺项的代数非退化亚纯映射，其中α&gt；0仅依赖于d。关于唯一性集的结果很多，但关于唯一性整环的结果似乎很少。我们将在C中找到一个无界区域，使得唯一性定理在该区域上受限的条件下成立。Mori，Lin和Tohge给出了一个关于角域上…的唯一性定理论文被提交了更多的时间。研究人员Aihara得到了映射是代数依赖的亚纯映射下因子的逆象的几个条件，以及两个解析分枝覆盖空间相等的条件。这是代数体函数唯一性定理的几何推广。Nakada研究了类似有理函数的Blachke乘积的复杂动力学，特别是Hausdorff维数的估计和Julia集在欧氏同余变换下的不变性。Sekigawa研究了作用在C上的Moebius变换序列的极限集，他还研究了作用在一般维空间上的Moebius变换。他还研究了利用克利福德矩阵的Moebius变换的一个表达式及其应用。Kawamura研究了概率密度函数的轨道，并通过计算机模拟给出了一组Tent映射上拓扑共轭映射的一个性质的证明。Sato推广了雅可比正交系与函数空间上的An算子和Hankel变换上的An算子之间的关系。Mizuhara证明了与广义Morrey空间上的函数、Block和Calderon-Zygmund算子有关的一个弱分解定理。较少

项目成果

RECENT TOPICS IN UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS

• DOI: 10.1007/1-4020-7951-6_13
• 发表时间: 2004
• 作者: Yoshihiro Aihara

Factorization of functions in H^1(R^n) and generalized Morrey spaces

H^1(R^n) 和广义 Morrey 空间中函数的因式分解

• 期刊: Math. Nachr. (掲載予定)
• 作者: Komori Yasuo;Mizuhara Takahiro
• 通讯作者: Mizuhara Takahiro

Deficiencies of meromorphic mappings for hypersurfaces

超曲面亚纯映射的缺陷

• 发表时间: 2005
• 期刊: J. Math. Soc. Japan 47
• 作者: Y.Aihara;S.Mori
• 通讯作者: S.Mori

Lorentz multipliers for Hankel transforms

汉克尔变换的洛伦兹乘子

• 发表时间: 2004
• 期刊: Scientiae Mathematicae Japonicae 59
• 作者: M.Belarbi;萬代武史;M.Mechab;Aihara Yoshihiro;K.Igari;Sato Enji
• 通讯作者: Sato Enji

Uniqueness problem for meromorphic mappings under conditions on the preimages of divisors

除数原像条件下亚纯映射的唯一性问题

• 发表时间: 2004
• 期刊: Advanced Studies in Pure Mathematics, Complex Analysis in Several Variables,(Mathematical Society of Japan) 42
• 作者: M.Belarbi;萬代武史;M.Mechab;Aihara Yoshihiro;K.Igari;Sato Enji;Mori Seiki;Aihara Yoshihiro;Aihara Yoshihiro;Sato Enji;T.Sadamatsu;Seiki Mori;Yoshihiro Aihara
• 通讯作者: Yoshihiro Aihara