Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials

被引：5

作者：

Berezin, Sergey ^{[1
,2
]}

Kuijlaars, Arno B. J. ^{[1
]}

Parra, Ivan ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200B box 2400, B-3001 Leuven, Belgium

[2] RAS, VA Steklov Math Inst, Fontanka 27, St Petersburg 191023, Russia

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2023年 / 19卷

关键词：

planar orthogonal polynomials; multiple orthogonal polynomials; Riemann-Hilbert problems; Hermite-Pade approximation; normal matrix model; RIEMANN-HILBERT PROBLEMS; ASYMPTOTICS; UNIVERSALITY; RESPECT;

D O I：

10.3842/SIGMA.2023.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a contour, provided the exponents in the weight are integer. From this orthogonality, we derive several equivalent Riemann-Hilbert problems. The proof is based on the fundamental identity of Lee and Yang, which we establish using a new technique.

引用

页数：18

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