2004 Fiscal Year Final Research Report Summary
Algebraic-analytical Study of non-local pseudo-differential equations in complex domains
| Project/Area Number |
15540155
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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.Tech., Professor, 工学部, 教授 (70155076)
TOSE Nobuyuki Keio University, Fac.Econ., Professor, 経済学部, 教授 (00183492)
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| Project Period (FY) |
2003 – 2004
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| Keywords | Algebraic analysis / Differential-difference equations / Pseudo-differential equations / Differential equations of infinite ordre / partial differential equations / Convolution equations / Microlocal analysis of sheaves / Cauchy problem |
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| Research Abstract |
The aims of this research were as follows :
[1]To study algebraic-analytically non-local pseudo-differential equations in complex domains.
[2]To construct holomorphic solutions to such equations and to establish the operational calculus.
[3]To study algebraic-analytically differential-differnce eqations in complex domains.
For [1], at first, we have defined cohomologically the classes of the non-local pseudo-differential operators operating to holomorphic functions defined at a fixed point, as well as their composition and the operation to functions. And secondly, using the Fourier-Sato transform, we re-defined the class of non-local pseudo-differential operators and proved functorially their composition. For [2], in the case of constant coefficient, we established a concrete integral representation formula for solutions to the non-local pseudo-differential equation, using the formal inverse operator. We also obtained concretely generators of the solution space of corresponding homogeneous equation. For [3], using the formula obtained in [2], we calculated special solutions to differential-difference equations with constant coefficient.
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Research Products
(12 results)
