2013 Fiscal Year Final Research Report
Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator
| Project/Area Number |
23540219
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 散乱逆問題 / 自己共役作用素 / 特異ランク1摂動 |
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| Research Abstract |
One of the most important problems in the scattering theory is the characterization of the scattering matrices. This investigation studies forward and inverse scattering problems for singular rank-one perturbations of a selfadjoint operator A. I obtain necessary and sufficient conditions for a function to be the phase shift of a singular rank-one perturbation of A. This result is closely related with the theory of point interactions.
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