Functional analysis and algebraic analysis of coupling theory

2022 Fiscal Year Final Research Report

• Project/Area Number: 16K05170
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Chiba University
• Principal Investigator: Okada Yasunori 千葉大学, 大学院理学研究院, 教授 (60224028)
• Project Period (FY): 2016-04-01 – 2023-03-31
• Keywords: coupling方程式 / 代数解析 / 関数解析 / 局所凸空間

Outline of Final Research Achievements

As for the coupling equations for nonlinear partial differential equations of normal type, we extended the theory to a wider class of equations, and discussed the solvability, the coupling transforms and their compositions, and the continuations. As for those for partial differential equations of Briot-Bouquet type, we also extended the theory to a wider class of equations, and introduced the diagonal embedding method. However, we made little progress on the symbol calculus.
Moreover, we studied the problem of continuous homomorphisms, generalized mean value operators, and some periodic boundary value problems.

Free Research Field

代数解析学

Academic Significance and Societal Importance of the Research Achievements

複素領域の非線形偏微分方程式の典型的なクラスである正規型およびBriot-Bouquet型の方程式に対するcoupling理論を拡張し、適用範囲を広げた。これはcoupling理論に関数解析的な視点と写像としての実体を与えるものであり、高い学術的意義を持つものである。