| Project/Area Number |
14540218
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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 | Ritsumeikan University |
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Principal Investigator |
YAMADA Osanobu Ritsumeikan Univ., Fac Science and Engineering, Professor, 理工学部, 教授 (70066744)
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| Co-Investigator(Kenkyū-buntansha) |
ITO Hiroshi Ehime University, Fac. Engineering, Associate Professor, 工学部, 助教授 (90243005)
SHINYA Hitoshi Ritsumeikan Univ., Fac. Science and Engineering, Professor, 理工学部, 教授 (70036416)
ARAI Masaharu Ritsumeikan Univ., Fac. Science and Engineering, Professor, 理工学部, 教授 (20066715)
OKAJI Takashi Kyoto University, Fac. Science, Associate Professor, 大学院・理学研究科, 助教授 (20160426)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | Dirac operator / Schroedinger operator / spectrum / eigenvalue / magnetic field / unique continuation property |
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| Research Abstract |
We investigated the spectraiTheoty of Dirac operators which appear in relativistic quantum mechanics. In particular, we are interested in the Dirac operator with potentials diverging at infinity. There are some differences in the spectral theoiy betweenDirac operators and Schmedinger operators. If potentials diverge to positive or negative infinity at infinity, the spectnim of Dirac operators cover the whole real line and have no eigenvalues, in general. Concerning the absence of eigenvalues H.Kalf, T. Okaji and 0.Yamada wrote
"Absence of elgenvalues of Dime operators with potentials diverging at infinity".
Under weaker conditions than above we studied that the spectrum covers the whole real line in
"A note on the essential spectwm of Schroedinger operators and Dime operators with magnetic fields and diverging potentials at inflnity" (Mem. Inst. Sci. Eng., Ritsumeikan Univ., 61,53-60,2002).
We have also studied the strong unique continuation property of Dime equations with M. Ikoma, a graduate student of Ritsumeikan University, and wrote
"Storong unique continuation property of two-dimensional Dirac equations with Aharonov-Bohm fields".
The investigators have also studied their own subjects extensively. T. Okaji extended the result on the absene of eigenvalues to Dirac type operators and investigated the absolute continuity of the spectrum of Dime operators. H.Ito investigated the scattering theoiy of Schmedinger operators. H. Shin'ya studied representation theoiy of locally compact motion groups.
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