2002 Fiscal Year Final Research Report Summary
Algebraic Analysis of Boundary Value Problems
| Project/Area Number |
12640188
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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 | Keio University |
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Principal Investigator |
TOSE Nobuyuki Keio University, Fac. of Economics, Professor, 経済学部, 教授 (00183492)
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| Project Period (FY) |
2000 – 2002
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| Keywords | Algebraic Analysis / Microlocal Analysis / Hyperfunctions / Microfunctions / Fourier Transform / D-module |
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| Research Abstract |
(I) Microfunctions with holomorphic parameters can be restricted with respect to a holomorphic parameter. Then a natural question arises. If all the trace with respect to a holomorphic parameters, is the microfunction with holomorphic parameters is equal to zero? I gave a solution of this question positively with O. Liess and Y. Okada.
(II) The 2-hyperfunctions is a natural object when we study 2^<nd> microlocalization. It contains a sheaf of microfunctions restricted to a regular involutive submanifold. I have characterized the gap between these two sheaves by means of inverse Fourier transformation.
(III) Let us consider the O-solution complex of a coherent D-module M. Then it is already well studied by Y. Laurent and T. Monteiro that the vanishing cycle of M can be used to construct a boundary value morphism. I studied the relation of their result with my former result on micro-hyperbolic problems.
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Research Products
(6 results)
