| Project/Area Number |
11440041
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
MIYAKE Masatake (2002) Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (70019496)
青本 和彦 (1999-2001) 名古屋大学, 大学院・多元数理科学研究科, 教授 (00011495)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NAKANISHI Tomoki Nagoya University, Graduate School of Mathematics, Associate professor, 大学院・多元数理科学研究科, 助教授 (80227842)
KIMURA Yoshihumi Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (70169944)
AOMOTO Kazuhiko Nagoya University, Graduate School of Mathematics, Emeritus Professor, 名誉教授 (00011495)
MINAMI Kazuhiko Nagoya University, Graduate School of Mathematics, Associate professor, 大学院・多元数理科学研究科, 教授 (40271530)
OKADA Soichi Nagoya University, Graduate School of Mathematics, Associate professor, 大学院・多元数理科学研究科, 助教授 (20224016)
三宅 正武 名古屋大学, 大学院・多元数理科学研究科, 教授 (70019496)
尾畑 伸明 名古屋大学, 大学院・多元数理科学研究科, 助教授 (10169360)
市原 完治 名古屋大学, 大学院・多元数理科学研究科, 助教授 (00112293)
行者 明彦 名古屋大学, 大学院・多元数理科学研究科, 教授 (50116026)
千代延 大造 名古屋大学, 大学院・多元数理科学研究科, 助手 (50197638)
|
|---|
| Project Period (FY) |
1999 – 2002
|
| Project Status |
Completed (Fiscal Year 2002)
|
| Budget Amount *help |
¥10,200,000 (Direct Cost: ¥10,200,000)
Fiscal Year 2002: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2001: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2000: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1999: ¥2,800,000 (Direct Cost: ¥2,800,000)
|
|---|
| Keywords | quasi hypergeometric / LR transform / orthogonal polynomials / divergent solution / Borel summability / singular equation / 形式的巾級数解 / 収束,発散 / ポアンカレ条件 / ジュブレイ指数 / 接続関係式 / 超球面配置 / 超幾何積分 / 差分方程式 / 接続行列 / Wu方程式 / 特異点 / モノドロミー / 離散可積分系 |
|---|
| Research Abstract |
K.Aomoto studied integral representation of special functions and obtained the following results :
1) He established an integral formulas for quasi hypergeometric functions and obtained monodromy formulas, and gave an explicit formula of singular point by using Picard-Lefschetz transform.
2) He extended the notion of LR transform and density matrices into multi dimensional case. More explicitly, he defined Gram-Schmidt orthogonal polynomials with a given density and he dfined its LR transform.
M.Miyake studied partial differential equatons in complex domain and obtained the following results :
3) He characterized the Borel summability of divergent formal solution of the Cauchy problem of certain non-Kowalevski type equations. He also gave an integral representation of the Borel sum.
4) He characterized a notion of singular equation or singular point for a nonlinear partial differential equation which depends on each solution. Moreover, the characterization of the singulaity is given by showing the convergent or the divergent criterion of the formal solutions.
|
