| Project/Area Number |
11640153
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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 FACULTY OF SCIENCES PROFESSOR, 理学部, 教授 (10127970)
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| Co-Investigator(Kenkyū-buntansha) |
AOKI Takashi KINKI UNIVERSITY, FAC.SCIE.TECH.PROFESSOR, 理工学部, 教授 (80159285)
OKADA Yasunori FACULTY OF SCIENCES ADJOINT PROFESSOR, 理学部, 助教授 (60224028)
HINO Yoshiyuki FACULTY OF SCIENCES PROFESSOR, 理学部, 教授 (70004405)
TOSE Nobuyuki KEIO UNIVERSITY, Fac. ECON.PROFESSOR, 経済学部, 教授 (00183492)
TAJIMA Shinichi NIIGATA UNIVERSITY, Fac. TECH.ADJOINTPROFESSOR, 工学部, 助教授 (70155076)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2000: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Algebraic analysis / Convolution equations / Pseudo-differential equations / Partial differential equations / Differential equations of infinite ordre / Micro-local study of sheaves / Canchy problem / 畳込み方程式 / 代数解析 |
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| Research Abstract |
The aims of this research were as follows :
[1] The algebraic-analytical study of convolution equations in the complex domains, using micro-local study of sheaves.
[2] Study of the Fabry-Ehrenpreis-Kawai Theorem, applying the theory of analytical continuation of solutions to convolution equations.
[3] The extension of the theory of the Cauchy problem for micro-differential equationts in the complex domains to the pseudo-differential case.
For the problem [1] and [2], at first, we constructed good examples of convolution equations with elliptic codition in the several variables. And also, for the problem of the analytic continuation of the holomorphic solutions to the homogeneous convolution equation in the complex domains, we introduced its characteristic sets to be the natural extension of the case of usual constant coefficients linear partial differential equations and we could present the expicit form of the domains to which any solution is continued analytically, using the characteristic set. In particular, this resolves almost completely the problem of the analytic continuation to the infinite ordre differential-difference equations which are important examples of the functional-differential equaion. In the case of tube domains, one proved that, in a natural condition, the characteristic set coincides with the accumulating directions at infinity of the zeros of the symbol. However, for [3], we did not yet succeed to get an general theory. But we are now studying the problem using the sheaf theoritical study by means of inductive limits which is in the course of developpement.
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