2002 Fiscal Year Final Research Report Summary
Analytic Integral and its applications
| Project/Area Number |
11440041
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
MIYAKE Masatake Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (70019496)
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| 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)
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| Project Period (FY) |
1999 – 2002
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| Keywords | quasi hypergeometric / LR transform / orthogonal polynomials / divergent solution / Borel summability / singular equation |
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| 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.
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