New developments of asymptotics for differential equations

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400114
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kobe University
• Principal Investigator: Koike Tatsuya 神戸大学, 理学研究科, 准教授 (80324599)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 完全WKB解析 / 漸近展開 / ボレル総和法 / 特異摂動 / Voros係数

Outline of Final Research Achievements

In this research we mainly studied Voros coefficients in exact WKB analysis, i.e., WKB method based on the Borel resummation method. Voros coefficients are one of the most important objects to study global behaviors of WKB solutions. We succeeded in clarifying the following topics: (1) the computation of Voros coefficients of singular perturbed higher order linear ordinary differential equations via the middle convolutions, (2) WKB theoretic studies of boosted operators using differential operators of infinite order, (3) the study of the exponential order of the Borel transform of WKB solutions of singular perturbed second order linear ordinary differential equations, and its relation to the multisummability.

Free Research Field

完全WKB解析