A Christoffel-Darboux formula for multiple orthogonal polynomials

被引：42

作者：

Daems, E ^{[1
]}

Kuijlaars, ABJ ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, B-3001 Louvain, Belgium

来源：

JOURNAL OF APPROXIMATION THEORY | 2004年 / 130卷 / 02期

关键词：

Christoffel-Darboux formula; multiple orthogonal polynomials; Riemann-Hilbert problem;

D O I：

10.1016/j.jat.2004.07.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a Christoffel-Darboux formula for this kernel for general multiple orthogonal polynomials. In addition, we show that the formula can be written in terms of the solution of the Riemann-Hilbert problem for multiple orthogonal polynomials, which will be useful for asymptotic analysis. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：190 / 202

页数：13

共 15 条

[1] Multiple orthogonal polynomials [J].

Aptekarev, AI .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1998, 99 (1-2) :423-447

[2] Multiple orthogonal polynomials for classical weights [J].

Aptekarev, AI ;

Branquinho, A ;

Van Assche, W .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (10) :3887-3914

[3]

Bleher PM, 2004, INT MATH RES NOTICES, V2004, P109

[4]

BLEHER PM, IN PRESS COMM MATH P

[5] Extension of level-spacing universality [J].

Brezin, E ;

Hikami, S .

PHYSICAL REVIEW E, 1997, 56 (01) :264-269

[6]

COUSSEMENT J, IN PRESS J COMPUT AP

[7]

Deift P A., 1999, ORTHOGONAL POLYNOMIA

[8] THE ISOMONODROMY APPROACH TO MATRIX MODELS IN 2D QUANTUM-GRAVITY [J].

FOKAS, AS ;

ITS, AR ;

KITAEV, AV .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 147 (02) :395-430

[9]

MAHLER K, 1968, COMPOS MATH, V19, P95

[10] ASYMPTOTICS OF DIAGONAL HERMITE-PADE POLYNOMIALS [J].

NUTTALL, J .

JOURNAL OF APPROXIMATION THEORY, 1984, 42 (04) :299-386

← 1 2 →