Asymptotic Analysis for Integrable Connections with Irregular Singular Points
Asymptotic Analysis for Integrable Connections with Irregular Singular Points
复制标题
不规则奇异点可积连接的渐近分析
DOI：
10.1007/bfb0071550
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
H. Majima
中科院分区：
文献类型：
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作者：
H. Majima
利用多变量函数的强渐近展开，我们证明了在某些一般条件下具有不规则奇点的一阶偏微分方程组可积系统渐近解的存在定理。我们还证明了完全可积线性普法夫系统的解析分裂引理。此外，对于不规则奇点的可积联系，我们制定并解决了Riemann-Hilbert-Birkhoff问题，并在某些一般条件下证明了Poincare引理和de Rham上同调定理的类似物。
Using strongly asymptotic expansions of functions of several variables, we prove existence theorems of asymptotic solutions to integrable systems of partial differential equations of the first order with irregular singular points under certain general conditions. We also prove analytic splitting lemmas for completely integrable linear Pfaffian systems. Moreover, for integrable connections with irregular singular points, we formulate and solve the Riemann-Hilbert-Birkhoff problem, and prove analogues of Poincare's lemma and de Rham cohomology theorem under certain general conditions.