Algebraic study of non-local differential equations and operational calculus
| Project/Area Number |
17540147
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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 | Chiba University |
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Principal Investigator |
ISHIMURA Ryuichi Chiba University, Faculty of Sciences, Professor, 理学部, 教授 (10127970)
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| Co-Investigator(Kenkyū-buntansha) |
HINO Yoshiyuki Chiba University, Faculty of Sciences, Professor, 理学部, 教授 (70004405)
OKADA Yasunori Chiba University, Faculty of Sciences, Associate Professor, 理学部, 助教授 (60224028)
AOKI Takashi Kinki University, Fac.Sci.Tech., Professor, 理工学部, 教授 (80159285)
TAJIMA Shin-ichi Niigata University, Fac.Sci.Tech., Professor, 工学部, 教授 (70155076)
TOSE Nobuyuki Keio University, Fac.Econ., Professor, 経済学部, 教授 (00183492)
筒井 亨 千葉大学, 理学部, 講師 (00197732)
渚 勝 千葉大学, 理学部, 教授 (50189172)
桜井 貴文 千葉大学, 理学部, 助教授 (60183373)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2006: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2005: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | Microlocal analysis of sheaves / Pseudo-differential equations / Infinite order differential equations / Operational calculus / Convolution equations / Differential-difference equations / Partial differential equations / Algebraic analysis / 非局所微分方程式 / 擬微分作用素 |
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| Research Abstract |
The aims of this research were as follows:
[1] Microlocal study of sheaves of non-local pseudo-differential operators.
[2] Construction of solutions and operational calculus, study of the solution space.
[3] Algeblaic analytical study of differential-difference equations by means of the theory of non-local pseudo-differential equations.
First for [1], we generalized the general theory of local pseudo-differential operators generalizing the Fourier-Sato transformation in the derived category on fiber bundle to the case having a move in the base space. Applying it to holomorphic differential forms on the cotangent bundle over a complex manifold, we obtained the complex of non-local pseudo-differential operators and taking its cohomology, we defined the sheaf of non-local pseudo-differential operators. We thus obtained composition of two such operators, considering functorially as above. Next, we established the notion of pseudo-differential operators operating to the stalk of holomorphic functions at a point, that is, an operator with the symbol such that its order as an entire function goes to 0 with the considered point.
For [2], and [3], we are going to investigate.
Furtheremore, we characterized continuous linear operator acting to the space of entire functions with given proximate ordre and a semi-norm as differential operator of infinite order.
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Report
(3 results)
Research Products
(10 results)
