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Mixed Type Hermite–Padé Approximants for a Nikishin System
Proceedings of the Steklov Institute of Mathematics ( IF 0.5 ) Pub Date : 2021-02-02 , DOI: 10.1134/s0081543820060127
V. G. Lysov

Abstract

We consider the problem of mixed type Hermite–Padé approximants and prove that the Nikishin system is perfect for this problem. Using the method of a vector equilibrium problem, we find weak asymptotics and prove the convergence of the approximants along any rays in the index table. We also present an equivalent statement in the form of a matrix Riemann–Hilbert problem.



中文翻译:

Nikishin系统的混合类型Hermite–Padé近似

摘要

我们考虑了混合型Hermite–Padé近似问题,并证明了Nikishin系统对于该问题是完美的。使用向量平衡问题的方法,我们找到了较弱的渐近性,并证明了指数表中沿所有光线的近似值的收敛性。我们还以矩阵黎曼–希尔伯特问题的形式提出了一个等价陈述。

更新日期:2021-02-02
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