A matrix characterization for the Dν-semiclassical and Dν-coherent orthogonal polynomials

Lino G. Garza; Luis E. Garza; Francisco Marcellán; Natalia C. Pinzón-Cortés

doi:10.1016/j.laa.2015.09.014

A matrix characterization for the Dν-semiclassical and Dν-coherent orthogonal polynomials

Lino G. Garza, Luis E. Garza, Francisco Marcellán, Natalia C. Pinzón-Cortés

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We present a new structure relation for the sequence of orthogonal polynomials associated with a ^Dν-semiclassical linear functional of class s, and then we use it to obtain a matrix characterization of the ^Dν-semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials, and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials. We also provide a matrix characterization of ^Dν-coherent pairs of linear functionals.

Original language	English
Pages (from-to)	242-259
Number of pages	18
Journal	Linear Algebra and Its Applications
Volume	487
DOIs	https://doi.org/10.1016/j.laa.2015.09.014
Publication status	Published - 15 Dec 2015
Externally published	Yes

Bibliographical note

Funding Information:
The work of the first author was supported by a grant of the Secretaría de Educación Pública of México and the Mexican Government. The work of the second author was supported by Consejo Nacional de Ciencia y Tecnología of México, grant 156668 . The work of the third author was supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain, grant MTM2012-36732-C03-01 . The authors thank the anonymous referee for her/his valuable comments and suggestions. They contributed to improve the presentation of the manuscript.

Publisher Copyright:
© 2015 Elsevier Inc. All rights reserved.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2015.09.014

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title = "A matrix characterization for the Dν-semiclassical and Dν-coherent orthogonal polynomials",

abstract = "We present a new structure relation for the sequence of orthogonal polynomials associated with a Dν-semiclassical linear functional of class s, and then we use it to obtain a matrix characterization of the Dν-semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials, and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials. We also provide a matrix characterization of Dν-coherent pairs of linear functionals. ",

author = "Garza, {Lino G.} and Garza, {Luis E.} and Francisco Marcell{\'a}n and Pinz{\'o}n-Cort{\'e}s, {Natalia C.}",

note = "Funding Information: The work of the first author was supported by a grant of the Secretar{\'i}a de Educaci{\'o}n P{\'u}blica of M{\'e}xico and the Mexican Government. The work of the second author was supported by Consejo Nacional de Ciencia y Tecnolog{\'i}a of M{\'e}xico, grant 156668 . The work of the third author was supported by Direcci{\'o}n General de Investigaci{\'o}n Cient{\'i}fica y T{\'e}cnica, Ministerio de Econom{\'i}a y Competitividad of Spain, grant MTM2012-36732-C03-01 . The authors thank the anonymous referee for her/his valuable comments and suggestions. They contributed to improve the presentation of the manuscript. Publisher Copyright: {\textcopyright} 2015 Elsevier Inc. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

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doi = "10.1016/j.laa.2015.09.014",

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AU - Garza, Lino G.

AU - Garza, Luis E.

AU - Marcellán, Francisco

AU - Pinzón-Cortés, Natalia C.

N1 - Funding Information: The work of the first author was supported by a grant of the Secretaría de Educación Pública of México and the Mexican Government. The work of the second author was supported by Consejo Nacional de Ciencia y Tecnología of México, grant 156668 . The work of the third author was supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain, grant MTM2012-36732-C03-01 . The authors thank the anonymous referee for her/his valuable comments and suggestions. They contributed to improve the presentation of the manuscript. Publisher Copyright: © 2015 Elsevier Inc. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2015/12/15

Y1 - 2015/12/15

N2 - We present a new structure relation for the sequence of orthogonal polynomials associated with a Dν-semiclassical linear functional of class s, and then we use it to obtain a matrix characterization of the Dν-semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials, and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials. We also provide a matrix characterization of Dν-coherent pairs of linear functionals.

AB - We present a new structure relation for the sequence of orthogonal polynomials associated with a Dν-semiclassical linear functional of class s, and then we use it to obtain a matrix characterization of the Dν-semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials, and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials. We also provide a matrix characterization of Dν-coherent pairs of linear functionals.

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SN - 0024-3795

VL - 487

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

A matrix characterization for the <sup>Dν</sup>-semiclassical and <sup>Dν</sup>-coherent orthogonal polynomials

Abstract

Bibliographical note

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