| Project/Area Number |
10640202
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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 |
Global analysis
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| Research Institution | Shinshu University |
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Principal Investigator |
ASADA Akira Faculty of Science, Shinshu University, Professor, 理学部, 教授 (00020652)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAYAMA Kazuaki Faculty of Science, Shinshu University, Research associate, 理学部, 助手 (20281040)
NISHIDA Kenji Faculty of Science, Shinshu University, Professor, 理学部, 教授 (70125392)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1999: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Spectre triple / Zeta-regularization / Dirac operator / Soboler space / Cohen-Macauley / AKNS inverse / Minkowski space / motion of curves / Spectre triple / Zeta-regularization / Sobolev space / AKNS inverse scattering schemes / Minkowski space / Mapping space / Infinite dimensional algebra / Clifford bundle / Spectre invariant / Zeta regularization / Integrable system |
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| Research Abstract |
1. Regularization of differential operation on a Halberd space.
Considering the pair of a Hilbert space H and some Kinds of Schatten class operator G on H, we propose a regularization of differential operators on H by using spectuer of G. We compile proper values and functions of regularized Loplacian and Dirac operator with suitable boundary conditions. We also clarify the meaning of zeta regularization and the relation of zeta regularization and infinite spinor adgoisred to the Cli Hord algebra over H by using this result.
2. Zeta regularized determinant of differential operators.
We solved a problem presented by Elizalde on the zeta regularized determinant of Dirac operators with mass-terms and give the relation between the sign of zeta regularized determinant and mass-term.
3. Study on Cohen-Macauley algebras.
Nisida studied algebras related to the thema of this project. Especially on the minimal injective resolution and Catenary and well studied.
4. Study on integrable equations.
Nakayama showed all integrable equations by the AKNS inverse scattering schemer are obtained from the movement of curves in a hyperboloid in the Minkowski space and gene its group theoretical reason.
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