RESEARCH OF VALUE DISTRIBUTION OF MEROMORPHIC MAPPINGS

亚形映射的值分布研究

• 批准号: 10640149
• 负责人: MORI Seiki
• 金额: $ 1.86万
• 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: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640149/
• 关键词: value distribution theory; meromorphic mapping; defect; moving target; unicity theorem; small function; Julia set; dynamical system for chaos; 特異積分作用素

The head investigator Mori researched a fewness of meromorphic mapping with defects. He obtained elimination theorems of defects of a meromorphic mapping into PィイD1nィエD1(C) by a small deformation, and also he proved that mappings without defects are dense in a space of transcendental meromorphic mappings. Investigator Toda obtained a unicity theorem for four small meromorphic functions, and also obtained a general form of Nevanlinna's second main theorem for a holomorphic curve into PィイD1nィエD1(C) and hyperplanes in subgeneral position. Nakada studied the local connectedness of Julia sets of hyperbolic rational maps and the number of non-conjugacy classes of non-repelling cycles of rational maps by using quasi-conformal surgery. Sekigawa studied finite order parabolic transformations with a torsion acting on RィイD13ィエD1 by using a Clifford matrix of Maebius transformations. Kazama proved a δδ-Lemma of Kodaira for some class of complex quasi-tori CィイD1nィエD1/Γ. Adachi obtained an extension … More theorem for a boundes holomorphic function on a subvariety V on a analytic polyhedra Ω in CィイD1nィエD1 to one on Ω. Kodama gave a characterization of certain weakly pseudo convex domains by using an extension theorem on holomorphic mappings and CR-mappings and applying Webster's CR-invariant metric, that is, he obtained conditions for which bounded domain in RィイD1nィエD1 is biholomorphic to a generalized complex ellipsoid. Kawamura studied chaotic maps on metric measure space using method of the theory of operator algebras and he obtained some important results concerning chaos and wavelet theory. Sato studied the space of Fourier multipliers on locally compact abelian groups. Also he studied on the transference of continuity from maximal Fourier multiplier operators on RィイD1nィエD1 to those on TィイD1nィエD1. Mizuhara proved the boundedness of commutators between some singular integral operator and multiplication operator by a loccaly integrable function on Morrey spaces with general growth function. Oakayasu obtained a theorem on a multivariable von Neumann's inequality. Less

首席研究员Mori研究了几种带缺陷的亚纯映射。他通过一个小的变形，得到了一个亚纯映射到P γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ (C)的缺陷的消去定理，并证明了在超越亚纯映射空间中没有缺陷的映射是密集的。研究者Toda得到了4个小亚纯函数的唯一性定理，并得到了关于全纯曲线在次一般位置上成P \ \ n \ \ \ \ D1(C)和超平面的Nevanlinna第二主定理的一般形式。Nakada利用拟共形手术研究了双曲有理映射的Julia集的局部连通性和有理映射的非排斥环的非共轭类的个数。Sekigawa利用mabius变换的Clifford矩阵研究了具有R * * * * * * * * * * * * * * *的有限阶抛物变换。Kazama证明了一类复拟环面C的δδ-引理。足立获得一个扩展 ... 更定理一个绑定亚变种V上全纯函数在分析多面体ΩCィイD1nィエD1 KodamaΩ。给某些弱拟凸域的特征通过一个扩展定理全纯映射和CR-mappings应用韦氏CR-invariant指标,也就是说,他获得条件有限域的RィイD1nィエD1双全纯的广义复椭球。Kawamura利用算子代数理论的方法研究了度量度量空间上的混沌映射，得到了混沌和小波理论的一些重要结果。佐藤研究了局部紧阿贝尔群上的傅里叶乘子空间。他还研究了从R上的最大傅立叶乘子算子到T上的最大傅立叶乘子算子的连续性转移。Mizuhara用一个具有一般生长函数的Morrey空间上的局部可积函数证明了奇异积分算子与乘法算子之间的交换子的有界性。Oakayasu获得了一个关于多变量von Neumann不等式的定理。少

项目成果

KODAMA Akio: "An application of Webster's CR-invariant metric to a characterization of generalized complex ellipsoids"Proc. of the Fifth Intern. Colloq. on Finite or Infinite Dimensional Complex Analysis, Beijing University. 173-176 (1998)

KODAMA Akio：“韦氏 CR 不变度量在广义复杂椭球表征中的应用”Proc。

M. Kaneko and E. Sato: "Notes on transference of continuity from maximal Fourier operators on RィイD1nィエD1 to those on TィイD1nィエD1"Interdiscriplinary Information Sciences. 4. 97-107 (1998)

M. Kaneko 和 E. Sato：“关于从 RiiD1nIeD1 上的最大傅里叶算子到 TiiD1nieD1 上的最大傅里叶算子的连续性转移的注释”跨学科信息科学 4. 97-107 (1998)。

A. Kodama: "An application of Webster's CR-invariant metric to a characterization of generalized complex ellipsoids"Proc. Of the Fifth Intern. Colloq. On Finite or Infinite Dimensional Complex Analysis, Beijing University. 173-176 (1998)

A. Kodama：“韦氏 CR 不变度量在广义复杂椭球表征中的应用”Proc。

T. Okayasu: "The Lowner-Hienz inequality in Banach *-Algebras."Glasgow Math. J.. 42. 243-246 (2000)

T.Okayasu：“Banach *-代数中的 Lowner-Hienz 不等式。”格拉斯哥数学。

MORI Seiki,: "Elimination of defects of meromorphic mappings of C^m into P^n(C),"Annales Academie Scientiarum Fennicae, Mathematica. Vol.24. 89-104 (1999)

MORI Seiki，：“消除 C^m 到 P^n(C) 的亚纯映射缺陷”，《Annales Academie Scientiarum Fennicae》，Mathematica。