New developments of asymptotics for differential equations
Project/Area Number |
25400114
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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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
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | 完全WKB解析 / 漸近展開 / ボレル総和法 / 特異摂動 / Voros係数 / 漸近解析 / 複素領域における常微分方程式論 / 代数解析 / Borel 総和法 / 多重総和法 / middle convolution / A超幾何方程式系 / 不確定特異点 / Borel総和法 / Voros 係数 / 無限階微分作用素 |
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.
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Report
(5 results)
Research Products
(15 results)