Spectral and scattering theory on geometric objects
| Project/Area Number |
25800073
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Kobe University (2014-2016)
University of Tsukuba (2013) |
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Principal Investigator |
Ito Kenichi 神戸大学, 理学研究科, 准教授 (90512509)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 関数方程式 / 多様体上での解析 / 数理物理 / 偏微分方程式論 / 差分作用素 / シュレーディンガー方程式 / 閾値レゾナンス / リーマン多様体 / スペクトル幾何 / 関数方程式論 |
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| Outline of Final Research Achievements |
I constructed a new general framework for the stationary scattering theory for the Schroedinger operator on a manifold with asymptotically Euclidean and/or hyperbolic funnel ends. I also succeeded in formulating the threshold resonances in a natural manner for the discrete Schroedinger operators on the discrete line and discrete half-line. Moreover, I obtained explicit expressions for the branching parts around thresholds for the resolvent of the discrete Laplacian on the square lattice.
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Report
(5 results)
Research Products
(43 results)
