2012 Fiscal Year Final Research Report
Study of Fuchsian system of differential equations from the view point of algebraic analysis and microlocal analysis
| Project/Area Number |
20540191
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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 |
Basic analysis
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| Research Institution | Nihon University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
AOKI Takashi 近畿大学, 理工学部, 教授 (80159285)
HONDA Naofumi 北海道大学, 理学研究院, 准教授 (00238817)
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| Project Period (FY) |
2008 – 2012
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| Keywords | 代数解析学 / 超局所解析学 / 佐藤超函数 / D加群 |
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| Research Abstract |
(1) If we impose an irregularity condition due to N. Honda for a system of analytic linear differential equations (D-Module), we can define non-characteristic initial and boundary values for the corresponding Gevrey function or ultradistribution solutions. Moreover, under a (weak) hyperbolicity condition, we can prove unique solvability theorems for Cauchy and boundary value problems.(2) For any regular-specializable system, we can define general boundary values for extensible distribution or ultradistribution solutions under an irregularity condition due to H. Tahara.(3) By a joint work with T. Aoki and N. Honda, we can establish new cohomological representation and symbol theory for pseudodifferetial operators of infinite order in analytic category.
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