Study of non-local differential equations and convolution equations in the complex domain

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540186
• 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: ISHIMURA Ryuichi 千葉大学, 理学(系)研究科(研究院), 教授 (10127970)
• Co-Investigator(Renkei-kenkyūsha): OKADA Yasunori 千葉大学, 大学院理学研究科, 教授 (60224028)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: 畳込み方程式 / 非局所微分方程式 / 包合的微分方程式系

Outline of Final Research Achievements

First we considered convolution equations with analytic-functional kernel in the space A-∞(D) of holomorphic functions with polynomial growth near the boundary of a convex domain D and we determined the directions to which any solutions to the corresponding homogeneous equation is prolongated. Secondely, we established the invertibility Theorem for a non-local differential equation and using this, we proved the existence and analytic continuation for the equation. As an application, we obtained the operational calculus for a differential-difference equation with constant coefficients.

Free Research Field

解析学