A Jacobi type Christoffel-Darboux formula for multiple orthogonal polynomials of mixed type

被引：6

作者：

Araznibarreta, Gerardo ^{[1
]}

Manas, Manuel ^{[1
]}

机构：

[1] Univ Complutense Madrid, Dept Fis Teor Metodos Matemat Fis 2, E-28040 Madrid, Spain

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 468卷

关键词：

Multiple orthogonal polynomials; Christoffel-Darboux formula; Moment matrices; Jacobi type matrices; Gauss decomposition; NONINTERSECTING BROWNIAN MOTIONS; RIEMANN-HILBERT PROBLEMS; RANDOM MATRICES; DISCRETE KP; HIERARCHY; PERFECT; SYSTEMS;

D O I：

10.1016/j.laa.2014.04.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An alternative expression for the Christoffel-Darboux formula for multiple orthogonal polynomials of mixed type is derived from the LU factorization of the moment matrix of a given measure and two sets of weights. We use the action of the generalized Jacobi matrix J, also responsible for the recurrence relations, on the linear forms and their duals to obtain the result. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：154 / 170

页数：17

共 50 条

[1] A Christoffel-Darboux formula for multiple orthogonal polynomials
Daems, E
Kuijlaars, ABJ
[J]. JOURNAL OF APPROXIMATION THEORY, 2004, 130 (02) : 190 - 202
[2] Generalized orthogonal polynomials and the Christoffel-Darboux formula
Geronimus, J
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES DE L URSS, 1940, 26 : 847 - 849
[3] On the Christoffel-Darboux formula for generalized matrix orthogonal polynomials
Alvarez-Fernandez, Carlos
Marnas, Manuel
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 418 (01) : 238 - 247
[4] A General Christoffel-Darboux Type Formula
Hugo J. Woerdeman
[J]. Integral Equations and Operator Theory, 2010, 67 : 203 - 213
[5] A General Christoffel-Darboux Type Formula
Woerdeman, Hugo J.
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2010, 67 (02) : 203 - 213
[6] Generalized Christoffel-Darboux formula for classical skew-orthogonal polynomials
Ghosh, Saugata
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (43)
[7] CHRISTOFFEL-DARBOUX FORMULA FOR ORTHOGONAL TRIGONOMETRIC POLYNOMIALS OF SEMI-INTEGER DEGREE
Milovanovic, Gradimir V.
Cvetkovic, Aleksandar S.
Stanic, Marija P.
[J]. FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2008, 23 : 29 - 37
[8] A Christoffel-Darboux formula and a Favard's theorem for orthogonal Laurent polynomials on the unit circle
Cruz-Barroso, R
González-Vera, P
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 179 (1-2) : 157 - 173
[9] Generalized Christoffel-Darboux formula for skew-orthogonal polynomials and random matrix theory
Ghosh, Saugata
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (28): : 8775 - 8782
[10] GENERALIZATIONS OF THE CHRISTOFFEL-DARBOUX IDENTITY FOR ADJACENT FAMILIES OF ORTHOGONAL POLYNOMIALS
BREZINSKI, C
[J]. APPLIED NUMERICAL MATHEMATICS, 1991, 8 (03) : 193 - 199

← 1 2 3 4 5 →