We continue studying the connection between Jacobi matrices defined on a tree and multiple orthogonal polynomials (MOPs) that was recently discovered. In this paper, we consider Angelesco systems formed by two analytic weights and obtain asymptotics of the recurrence coefficients and strong asymptotics of MOPs along all directions (including the marginal ones). These results are then applied to show that the essential spectrum of the related Jacobi matrix is the union of intervals of orthogonality.

中文翻译：

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由Angelesco系统生成的树上的雅可比矩阵：系数和基本谱的渐近

我们继续研究在树上定义的 Jacobi 矩阵与最近发现的多个正交多项式 (MOP) 之间的联系。在本文中，我们考虑由两个解析权重形成的Angelesco系统，并获得沿所有方向（包括边缘方向）的递归系数的渐近和MOP的强渐近。然后应用这些结果来表明相关雅可比矩阵的本质谱是正交区间的并集。