2010 Fiscal Year Final Research Report
The characterization of the closed range operator and the invariant subspace using the sampling set
| Project/Area Number |
20740070
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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 | Otaru University of Commerce |
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Principal Investigator |
YONED Rikio Otaru University of Commerce, 商学部, 准教授 (70342475)
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| Project Period (FY) |
2008 – 2010
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| Keywords | ベルグマン空間 / ハーディー空間 / 荷重付きディクレ空間 / 閉値域 / 掛け算作用素 / サンプリング集合 / テープリッツ作用素 / 積分作用素 / ハンケル作用素 / 不変部分空間 |
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| Research Abstract |
I researched the operators on the weighted Dirichlet spaces. In particular, I studied the multiplication operator and the Toeplitz operator and the Hankel operator on the weighted Dirichlet space with the closed range. It is well-known with respect to the closed range multiplication operator, but there is no result with respect to the closed range Toeplitz operator and Hankel operator on the weighted Dirichlet space. So I studied the sampling set with respect to the analytic symbol multiplication operator. Moreover I get the results when Toeplitz operator and Hankel operator have the closed range on the weighted Dirichlet spaces.
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[Presentation] The composition operator with closed range on the weighted Bloch space and the weighted Drichlet spaces
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[Presentation] Composition operators on the weighted Dirichlet spaces with closed range
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[Presentation] The characterizarion of the sampling set for Bloch-type spaces
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[Presentation] Interpolation sequence and closed range integration operator
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[Presentation] The multiplication operators on the weighted Dirichlet spaces
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[Presentation] The lower norm of the multiplication operators
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[Presentation] Hankel operator with closed range
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[Presentation] 閉値域をもつハンケル作用素に関して
