从二维Toda层次到黎曼球面区域的共形映射
From 2D Toda hierarchy to conformal map for domains of Riemann sphere
AI总结：
本文研究二维Toda层次无色散极限弦解泰勒级数的性质，给出了其收敛的充分条件，该弦解用于计算黎曼球面区域的单叶共形映射。
摘要：
在近期工作[hep-th/9909147, hep-th/0005259]中，发现了可积系统与亚纯函数之间的奇妙关联。它们将关于共形映射的黎曼定理的有效化问题，归结为二维Toda层次无色散极限的弦解的计算。在[math.CV/0103136]中，找到了弦解的泰勒级数系数的递推公式。这尤其提供了一种方法，用于计算从单位圆盘到由调和矩描述的任意区域的单叶共形映射。在本文中，我们研究了这些公式的某些性质。特别地，我们找到了二维Toda层次无色散极限的弦解的泰勒级数收敛的一个充分条件。
英文摘要：
In recent works [hep-th/9909147, hep-th/0005259] was found a wonderful correlation between integrable systems and meromorphic functions. They reduce a problem of effictivisation of Riemann theorem about conformal maps to calculation of a string solution of dispersionless limit of the 2D Toda hierarchy. In [math.CV/0103136] was found a recurrent formulas for coeffciens of Taylor series of the string solution. This gives, in particular, a method for calculation of the univalent conformal map from the until disk to an arbitrary domain, described by its harmonic moments. In the present paper we investigate some properties of these formulas. In particular, we find a sufficient condition for convergence of the Taylor series for the string solution of dispersionless limit of 2D Toda hierarchy.
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