Christoffel functions for multiple orthogonal polynomials

被引：1

作者：

Swiderski, Grzegorz ^{[1
,2
]}

Van Assche, Walter ^{[1
]}

机构：

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

[2] Univ Wroclaw, Fac Math & Comp Sci, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

来源：

JOURNAL OF APPROXIMATION THEORY | 2022年 / 283卷

基金：

比利时弗兰德研究基金会;

关键词：

Multiple orthogonal polynomials; Christoffel-Darboux kernel; Zero distribution; Nevai?s operators; ASYMPTOTIC ZERO DISTRIBUTION; GAUSSIAN QUADRATURE; RANDOM MATRICES; UNIVERSALITY; ENSEMBLES; SYSTEMS; LIMIT;

D O I：

10.1016/j.jat.2022.105820

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study weak asymptotic behaviour of the Christoffel-Darboux kernel on the main diagonal corresponding to multiple orthogonal polynomials. We show that under some hypotheses the weak limit of n1 Kn(x, x) d mu is the same as the limit of the normalized zero counting measure of type II multiple orthogonal polynomials. We also study an extension of Nevai's operators to our context.(c) 2022 Elsevier Inc. All rights reserved.

引用

页数：22

共 50 条

[21] DARBOUX-CHRISTOFFEL GENERALIZED FORMULA FOR ORTHOGONAL POLYNOMIALS
LASCOUX, A
HE, S
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1985, 300 (20): : 681 - 683
[22] 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
[23] CHRISTOFFEL FUNCTIONS AND UNIVERSALITY LIMITS FOR ORTHOGONAL RATIONAL FUNCTIONS
Deckers, Karl
Lubinsky, Doron S.
[J]. ANALYSIS AND APPLICATIONS, 2012, 10 (03) : 271 - 294
[24] Multiple orthogonal polynomials associated with confluent hypergeometric functions
Lima, Helder
Loureiro, Ana
[J]. JOURNAL OF APPROXIMATION THEORY, 2020, 260
[25] CHRISTOFFEL FUNCTIONS, ORTHOGONAL POLYNOMIALS, AND NEVAIS CONJECTURE FOR FREUD WEIGHTS (VOL 8, PG 463, 1992)
LEVIN, AL
LUBINSKY, DS
[J]. CONSTRUCTIVE APPROXIMATION, 1995, 11 (03) : 417 - 418
[26] DEK-type orthogonal polynomials and a modification of the Christoffel formula
Bailey, Rachel
Derevyagin, Maxim
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 438
[27] A CONTINUAL ANALOGUE OF A CHRISTOFFEL FORMULA FROM THE THEORY OF ORTHOGONAL POLYNOMIALS
KREIN, MG
[J]. DOKLADY AKADEMII NAUK SSSR, 1957, 113 (05): : 970 - 973
[28] 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
[29] How poles of orthogonal rational functions affect their Christoffel functions
Deckers, Karl
Lubinsky, Doron S.
[J]. JOURNAL OF APPROXIMATION THEORY, 2012, 164 (09) : 1184 - 1199
[30] On Christoffel type functions for Lm extremal polynomials, II
Shi, YG
[J]. JOURNAL OF APPROXIMATION THEORY, 2001, 111 (01) : 59 - 80

← 1 2 3 4 5 →