2013 Fiscal Year Final Research Report
Study on vector bundles induced by module structure of reproducing kernel Hilbert spaces consisting of multivariable analytic functions
| Project/Area Number |
23740106
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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 |
Basic analysis
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| Research Institution | Shimane University |
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Principal Investigator |
SETO Michio 島根大学, 総合理工学研究科(研究院), 准教授 (30398953)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 再生核ヒルベルト空間 / ハーディ空間 / 多変数作用素論 / グラフ理論 |
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| Research Abstract |
1. A certain class of self-adjoint operators is induced by submodules of the Hardy space over the bidisk. These operators are called defect operators. We studied eigenvalues and eigenfunctions of defect operators perturbed by biholomorphic maps.
2. A class of reproducing kernel Hilbert spaces can be constructed from graphs by a canonical way. We studied relation between their Gram matrices and Laplace matrices. Further, we introduced de Branges-Rovnyak theory into graph theory, and showed that it would be an appropriate framework dealing with graph homomorphisms.
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