| Project/Area Number |
15540185
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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, Faculty of Economics, Professor, 経済学部, 教授 (00183492)
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| Project Period (FY) |
2003 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | microlocal analysis / Fourier integral operators / micro-hyperbolicity / second microlocalization / conical refraction / microfunction / hyperfunctions / crystal optics / conical refraction / 多曲型方程式 / 積分幾何 / 特異積分作用素 / 変換理論 / 双曲型方程式 / 作用素の標準形 / 標準形 / 代数解析 / Conical refraction |
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| Research Abstract |
In the study of propagation of (microlocal) singularities of solutions to linear hyperbolic equations, a variety of phenomenon such as branching of singularities and conical refraction. In particular, conical refraction has been studied from many points of vies since it appeared naturally in natural world. Around 1885, in the study of conical refraction, the method of second microlocalization was employed, which blow-up the phase space along an involutive submanifold. This made it possible to obtain a certain successful result by P. Laubin and N. Tose. But there still remained some problems as far as existence of solutions is concerned. In this research, a transformation theory for operators in the category of second microlocalization is constructed.
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