Coherent pairs and Sobolev-type orthogonal polynomials on the real line: An extension to the matrix case

被引：1

作者：

Fuentes, Edinson ^{[1
]}

Garza, Luis E. ^{[2
]}

机构：

[1] Univ Pedag & Tecnol Colombia, Escuela Matemat & Estadist, Ave Cent Norte 39-115, Tunja, Boyaca, Colombia

[2] Univ Colima, Fac Ciencias, Bernal Diaz Castillo 340, Colima, Mexico

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 518卷 / 01期

关键词：

Matrix orthogonal polynomials; Matrix coherent pairs; Matrix Sobolev polynomials; LAGUERRE; ASYMPTOTICS; RESPECT;

D O I：

10.1016/j.jmaa.2022.126674

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this contribution, we extend the concept of coherent pair for two quasi-definite matrix linear functionals u0 and u1. Necessary and sufficient conditions for these functionals to constitute a coherent pair are determined, when one of them satisfies a matrix Pearson-type equation. Moreover, we deduce algebraic properties of the matrix orthogonal polynomials associated with the Sobolev-type inner product(sic)p, q(sic)(s) = (sic)p,q(sic)(u0) + (sic)p'M-1, q'M-2(sic)(u1) ,where M-1 and M-2 are m x m non-singular matrices and p, q are matrix polynomials.(c) 2022 Elsevier Inc. All rights reserved.

引用

页数：21

共 50 条

[1] COHERENT PAIRS AND ZEROS OF SOBOLEV-TYPE ORTHOGONAL POLYNOMIALS
MEIJER, HG
[J]. INDAGATIONES MATHEMATICAE-NEW SERIES, 1993, 4 (02): : 163 - 176
[2] SOBOLEV-TYPE ORTHOGONAL POLYNOMIALS - THE NONDIAGONAL CASE
ALFARO, M
MARCELLAN, F
REZOLA, ML
RONVEAUX, A
[J]. JOURNAL OF APPROXIMATION THEORY, 1995, 83 (02) : 266 - 287
[3] On sobolev orthogonal polynomials with coherent pairs: The Laguerre case, type 1
Pan, K
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 223 (01) : 319 - 333
[4] On Sobolev orthogonal polynomials with coherent pairs the Jacobi case
Pan, K
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 79 (02) : 249 - 262
[5] Asymptotics for Sobolev orthogonal polynomials with coherent pairs: The Jacobi case, type 1
Pan, K
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (08) : 2377 - 2388
[6] Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Jacobi type
Delft Univ of Technology, Delft, Netherlands
[J]. J Comput Appl Math, 1 (87-97):
[7] Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Laguerre type
Meijer, HG
Pérez, TE
Piñar, MA
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 245 (02) : 528 - 546
[8] Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Jacobi type
Meijer, HG
Piñar, MA
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1999, 108 (1-2) : 87 - 97
[9] Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case
Marcato, G. A.
Marcellan, F.
Ranga, A. Sri
Lun, Yen Chi
[J]. STUDIES IN APPLIED MATHEMATICS, 2023, 151 (02) : 475 - 508
[10] Sobolev-type orthogonal polynomials on the unit circle
Marcellán, F
Moral, L
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2002, 128 (2-3) : 329 - 363

← 1 2 3 4 5 →