Research of complex functional equations by means of theory of meromorphic functions
| Project/Area Number |
22540233
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Nippon Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
MORI Seiki 山形大学, 理学部, 教授 (80004456)
SHIMOMURA Shun 慶應義塾大学, 理工学部, 教授 (00154328)
MOROSAWA Shunsuke 高知大学, 理学部, 教授 (50220108)
TOHGE Kazuya 金沢大学, 理工学域, 教授 (30260558)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 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 |
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| Research Abstract |
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.
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Report
(4 results)
Research Products
(11 results)
