We study a two-dimensional vector logarithmic-potential equilibrium problem with the Nikishin matrix of interaction. A constructive method for finding the supports of a vector equilibrium measure is given. The densities of the components of the equilibrium measure are expressed in terms of an algebraic function that is explicitly written out. The problem is motivated by the study of the convergence of the Frobenius–Pade and Hermite–Pade rational approximants.

中文翻译：

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一向量平衡问题的构造解

我们研究了具有相互作用的 Nikishin 矩阵的二维向量对数电位平衡问题。给出了寻找向量平衡测度的支持的构造方法。均衡测度的分量的密度用明确写出的代数函数表示。该问题的动机是研究 Frobenius-Pade 和 Hermite-Pade 有理近似的收敛性。