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植田 優基
ウエダ ユウキ UEDA Yuki 所 属 旭川校 職 名 准教授 |
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| 言語種別 | 日本語 |
| 発行・発表の年月 | 2025/05/01 |
| 形態種別 | 学術雑誌 |
| 標題 | Higher-order asymptotic expansion with error estimate for the multidimensional Laplace-type integral under perturbations |
| 執筆形態 | 共著 |
| 掲載誌名 | arXiv:2504.01310 |
| 掲載区分 | 国外 |
| 著者・共著者 | Ikki Fukuda, Yoshiki Kagaya, Yuki Ueda |
| 概要 | We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous results including Laplace's method. The key points of the proof are a precise asymptotic analysis based on a lot of detailed Taylor expansions, and a careful consideration of the effects of the perturbations on the Hessian matrix of the phase function. |