Research of complex functional equations by means of theory of meromorphic functions

利用亚纯函数理论研究复函数方程

• 批准号: 22540233
• 负责人: ISHIZAKI Katsuya
• 金额: $ 1.91万
• 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: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540233/
• 关键词: 関数方程式の大域理論; 有理型函数論; 差分方程式; 整函数論; Nevanlinna理論; Wiman-Valiron理論; q-差分方程式; 差分Riccati方程式; 増大の位数; テーラー展開; 複素力学系; 複素振動; Schroeder方程式

We are concerned with meromorphic solutions of some functional equations in the complex plane. We obtained a relation between difference Riccati equations and linear difference equations of second order, and also investigated the existence of meromorphic solutions to some functional equations and the order of growth of meromorphic solutions. Further, we considered the properties of meromorphic functions of small order. The general form of the Valiron-Mokhon’ko theorem is established. We applied this result to Schroder type functional equations. The relation between the coefficients of an entire function and the order of growth is obtained in order to investigate the existence of entire solution of linear q-difference equations.

研究复平面上某些泛函方程的亚纯解。得到了差分Riccati方程与二阶线性差分方程之间的关系，并研究了某些泛函方程亚纯解的存在性和亚纯解的生长阶。进一步研究了小阶亚纯函数的性质。建立了Valiron-Mokhon 'ko定理的一般形式。我们将这一结果应用于Schroder型泛函方程。为了研究线性q差分方程全解的存在性，得到了整个函数的系数与增长阶的关系。

项目成果

Meromorphic solutions of functional equations f(G(z))=R(f(z))

函数方程的亚纯解 f(G(z))=R(f(z))

• 发表时间: 2011
• 期刊: Complex Var.Elliptic Equ.
• 作者: K.Ishizaki;S.Morosawa
• 通讯作者: S.Morosawa

複素差分方程式と値分布理論について

关于复差分方程和值分布理论

• 发表时间: 2012
• 作者: ASAKURA;Fumioki and Corli;Andrea;石崎克也
• 通讯作者: 石崎克也

Entire functions of small order of growth

小增长阶的全部函数

• 发表时间: 2009
• 作者: H. Mikami;Y. Sato;T. Matsumoto;and T. Hanawa;石崎克也
• 通讯作者: 石崎克也

On logarithmic order of an entire function in terms of the coefficients

关于整个函数的系数的对数阶

• 期刊: Proceedings of the American Mathematical Society
• 影响因子: 1
• 作者: K.Ishizaki;K.Tohge
• 通讯作者: K.Tohge

On difference Riccati equations and second order linear difference equations

• DOI: 10.1007/s00010-010-0060-z
• 发表时间: 2011-01
• 期刊: Aequationes mathematicae
• 影响因子: 0.8
• 作者: K. Ishizaki