anar正交多项式为I型多重正交多项式

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-12-13 DOI:10.3842/SIGMA.2023.020

S. Berezin, A. Kuijlaars, Iv'an Parra

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引用次数: 1

摘要

李（S.-Y.Lee）和杨（M.Yang）最近的一个结果指出，相对于修正的高斯测度正交的平面正交多项式是复平面中轮廓上的多个II型正交多项式。我们证明了同样的多项式也是轮廓上的I型正交多项式，前提是权重中的指数是整数。从这个正交性出发，我们导出了几个等价的黎曼-希尔伯特问题。证明是基于李和杨的基本身份，我们使用一种新的技术来建立这一身份。

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anar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials

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.

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.