Study of non-local differential equations and convolution equations in the complex domain
| Project/Area Number |
23540186
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Chiba University |
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Principal Investigator |
ISHIMURA Ryuichi 千葉大学, 理学(系)研究科(研究院), 教授 (10127970)
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| Co-Investigator(Renkei-kenkyūsha) |
OKADA Yasunori 千葉大学, 大学院理学研究科, 教授 (60224028)
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 畳込み方程式 / 非局所微分方程式 / 包合的微分方程式系 / 非局所擬微分方程式 / 演算子法 / 特性集合 / 微分・差分方程式 / 代数解析学 / 包合系 |
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| Outline of Final Research Achievements |
First we considered convolution equations with analytic-functional kernel in the space A-∞(D) of holomorphic functions with polynomial growth near the boundary of a convex domain D and we determined the directions to which any solutions to the corresponding homogeneous equation is prolongated. Secondely, we established the invertibility Theorem for a non-local differential equation and using this, we proved the existence and analytic continuation for the equation. As an application, we obtained the operational calculus for a differential-difference equation with constant coefficients.
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Report
(6 results)
Research Products
(6 results)
