两个复时间变量中某初值问题的形式解与强渐近展开、无穷阶不规则奇点及Mahler变换
Formal solution and strong asymptotic expansion of some initial value problem in two complex time variables, infinite order irregular singularities and Mahler transforms
- Universidad de Alcalá（阿尔卡拉大学）
- University of Lille（里尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过不动点论证构造了含Mahler型算子的无穷阶偏微分方程的形式解，并证明其双变量Laplace变换沿多方向具有强渐近展开。
AI中文摘要：
本文获得了涉及多个变量中Mahler型算子作用的无穷阶偏微分方程的形式解。此类形式解是通过对已发展的多变量减速算子的积分表示应用不动点论证而构造的。相关问题在Borel平面和Fourier空间中的实际解的双变量Laplace变换，被证明沿适当的多方向允许强渐近展开。
英文摘要：
A formal solution to a partial differential equation of infinite order involving the action of Mahler-type operators in several variables is obtained. Such formal solutions is constructed by means of a fixed point argument applied to the integral representation of the deceleration operator in several variables that has been developed. The Laplace transform in two variables of the actual solution of a related problem in both Borel plane and Fourier space turns out to admit strong asymptotic expansion along adequate multidirections.
