Operator analysis and its application on the weighted Bergman spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540155
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Otaru University of Commerce
• Principal Investigator: YONEDA Rikio 小樽商科大学, 商学部, 准教授 (70342475)
• Co-Investigator(Renkei-kenkyūsha): NAKAZI Takahiko 北星学園大学, 教授 (30002174) ; YAMAMOTO Takanori 北海学園大学, 工学部, 教授 (60182630) ; YAMADA Masahiro 岐阜大学, 教育学部, 准教授 (00263666) ; SETO Micho 島根大学, 総合理工学研究科, 准教授 (30398953)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ベルグマン空間 / テープリッツ作用素 / 閉値域 / 合成作用素 / 逆不等式

Outline of Final Research Achievements

I researched the operators on the weighted Dirichlet spaces. In particular, I studied 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.

Free Research Field

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