2012 Fiscal Year Final Research Report
Singularities of the Schrodinger equation
| Project/Area Number |
21740090
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
ITO Kenichi 筑波大学, 数理物質系, 講師 (90512509)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 関数方程式 |
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| Research Abstract |
I discussed the propagation of singularities and the spectral and scattering theory for the Schrodinger operator on a noncompact manifold with ends. Iextended results on the Euclidean space to those manifolds and studied what geometric structure is essentially needed for such analysis. I found that the existence of an endand its volume growth rate can be rephrased in terms of the existence of an unbounded convex function and its strength of convexity, respectively, and formulated geometrically, without coordinates, one model manifold on which methods of the Schrodinger operator theory applies.
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