| 研究課題/領域番号 |
21F21020
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| 配分区分 | 補助金 |
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| 研究機関 | 東京都立大学 |
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| 外国人特別研究員 |
ネメシュ ゲルグ 東京都立大学, 理学研究科, 特任准教授 (20994495)
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| 研究期間 (年度) |
2021-11-18 – 2024-03-31
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| キーワード | asymptotics / resurgence / exact WKB analysis / Borel summability |
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| 研究実績の概要 |
We have established the Borel summability of formal solutions for a broad class of higher-order linear ODEs with a large parameter. The problem of Borel summability for formal solutions of such equations has posed a longstanding challenge in the field of exact asymptotics. A manuscript summarising these results is currently under review. Furthermore, we investigated the resurgence properties of the incomplete gamma function in the transition region by analysing the asymptotics of the late coefficients in its asymptotic expansion. The findings have been published in the journal SIGMA. Prior to this paper, there has been no investigation in the existing literature regarding the resurgence properties of asymptotic expansions in transition regions.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
The research progressed smoothly. We have demonstrated the Borel summability of formal solutions for a wide range of higher-order linear ODEs with a large parameter. The issue of Borel summability for formal solutions of these equations has been a longstanding challenge in the field of exact asymptotics.
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| 今後の研究の推進方策 |
We aim to establish Borel summability for a broader class of equations where the characteristic equation is not a simple monomial. Additionally, we seek to derive connection formulas across Stokes lines.
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