AI 中文总结
本文研究具有对称性的多连通域的复格林函数，借助Walsh共形映射简化其形式，用Jacobi椭圆函数和theta函数表示两实区间补集的复格林函数，得到双纽线域参数，提出更准确的共形映射数值计算方法。
AI 中文摘要
本文的研究目标有三个：（i）研究具有对称性的多连通域的复格林函数（实格林函数的解析延拓），借助Walsh共形映射将其转化为简单形式，映射到双纽线域；（ii）针对两个实区间的并集的补集，借助Jacobi椭圆函数和theta函数表示复格林函数；（iii）利用该表示，明确得到对应于两个区间补集的双纽线域的所有参数。此外，利用对应复格林函数之间的等式，得到一种计算从两个区间补集到双纽线域的共形映射的数值方法，该方法比文献中已有方法的结果更准确。
英文摘要
The aim of this paper is threefold: (i) We study the complex Green's function (the analytic extension of the real Green's function) for multiply connected domains with some symmetry and transform it to a simple form with the help of Walsh's conformal map onto lemniscatic domains. (ii) For the complement of the union of two real intervals, we represent the complex Green's function with the help of Jacobi's elliptic and theta functions. (iii) Using this representation, we explicitly obtain all parameters of the lemniscatic domain corresponding to the complement of the two intervals. In addition, using an equality between the corresponding complex Green's functions, we obtain a numerical method for computing the conformal map from the complement of two intervals onto a lemniscatic domain which yields more accurate results than a previous method from the literature.
Journal refJournal of Mathematical Analysis and Applications, 565(2) (2026), 130976
DOI：10.1016/j.jmaa.2026.130976
