2009 Fiscal Year Final Research Report

Meromorphic solutions of discrete functional equations

Research Project

Project/Area Number	19540225
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Global analysis
Research Institution	Nippon Institute of Technology
Principal Investigator	ISHIZAKI Katsuya Nippon Institute of Technology, 工学部, 教授 (60202991)
Co-Investigator(Kenkyū-buntansha)	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, 准教授 (30260558)
Project Period (FY)	2007 – 2009
Keywords	差分方程式 / q-差分方程式 / Schroeder方程式 / Composite函数方程式 / Nevanlinna理論 / 複素力学系 / Wiman-Valiron理論 / 半共役
Research Abstract	We consider functional equations in the complex domains by means of the value distribution theory. In particular, discrete functional equations are discussed, for examples, difference equations and Schroeder equations. To do this, we are concerned with the growth of the composition of entire functions of slow growth. We obtain an estimate for composite functions without exceptional set. As an application, we apply this estimate to a Schroeder equation with a transcendental function. We also consider a functional equation f(G(z))=R(f(z)) from the view points of complex dynamics. By visualizations of some examples for known result, we posed a question. We solve it in general.

(7 results)