Topological structures for semiclosed operators using de Branges space theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540160
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Ibaraki University
• Principal Investigator: HIRASAWA GO 茨城大学, 工学部, 教授 (10434002)
• Co-Investigator(Kenkyū-buntansha): OKA Hirokazu 茨城大学, 工学部, 教授 (90257254)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 半閉作用素 / DeBranges空間 / 準線形発展方程式 / 強解

Outline of Final Research Achievements

We study the theory of semiclosed operators in a Hilbert space from the topological view point. We showed that the set of selfadjoint operators is relatively open in the set of semiclosed symmetric operators. From this result, a radius of a ball of a selfadjoint operator is considered naturally, and we give the value of a radius of a ball of Laplacian. This means that semiclosed symmetric operators which is in a ball of Laplacian having the radius as above automatically selfadjoint. As an application, we show the selfadjointness of Schrodinger operators with Kato-Rellich potential from the topological view point.

Free Research Field

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