Mixed Type Hermite-Pade Approximants for a Nikishin System

被引：10

作者：

Lysov, V. G. ^{[1
]}

机构：

[1] Russian Acad Sci, Keldysh Inst Appl Math, Miusskaya Pl 4, Moscow 125047, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2020年 / 311卷 / 01期

关键词：

mixed type Hermite– Padé approximants; Nikishin system; perfect system; vector logarithmic-potential equilibrium problem; convergence of rational approximants; matrix Riemann– Hilbert problem; STRONG ASYMPTOTICS; ORTHOGONAL POLYNOMIALS;

D O I：

10.1134/S0081543820060127

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem of mixed type Hermite-Pade 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.

引用

页码：199 / 213

页数：15

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