Operator analysis on Bergman space

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K03268
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Kanazawa University
• Principal Investigator: Rikio Yoneda 金沢大学, 学校教育系, 教授 (70342475)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: composition operator / Toeplitz operator / Bergman空間 / ディリクレ空間 / ベリジン変換 / 合成関数

Outline of Final Research Achievements

Bergman spatial theory is being advanced mainly by researchers in the United States, South Korea, and China, but most of their research is generalizing already known results (Hardy spatial theory). Against this backdrop, the applicant's current and future research is innovative and unbound by past trends. Specifically, we will derive a direct relationship between theories on Hardy space and Bergmann space, and derive a completely new characterization of weighted Dirichlet space (ultimately Functional Hilbert space, which is a general analytic function space). I am confident that this research will become a foundation for future work in related fields.

Free Research Field

函数論、作用素論

Academic Significance and Societal Importance of the Research Achievements

今回の研究成果の学術的意義としては、解析空間上の作用素に関する研究の基礎として非常に重要な結果を得られたことにある。得られた結果はどれも他分野に応用が期待できる基礎論として重要な成果でありすでに幾つか引用論文として取りあげられていることからもわかるが、解析学の多くの分野に今後引用されると考えている。