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

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Abstract

© 2015 Elsevier Inc. All rights reserved. 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
DOIs	https://doi.org/10.1016/j.laa.2015.09.014
Publication status	Published - 15 Dec 2015
Externally published	Yes

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All Science Journal Classification (ASJC) codes

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

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Garza, L. G., Garza, L. E., Marcellán, F., & Pinzón-Cortés, N. C. (2015). A matrix characterization for the Dν-semiclassical and Dν-coherent orthogonal polynomials. Linear Algebra and Its Applications, 242-259. https://doi.org/10.1016/j.laa.2015.09.014

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abstract = "{\textcopyright} 2015 Elsevier Inc. All rights reserved. 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.}",

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

language = "English",

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AU - Garza, Lino G.

AU - Garza, Luis E.

AU - Marcellán, Francisco

AU - Pinzón-Cortés, Natalia C.

PY - 2015/12/15

Y1 - 2015/12/15

N2 - © 2015 Elsevier Inc. All rights reserved. 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 - © 2015 Elsevier Inc. All rights reserved. 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.

U2 - 10.1016/j.laa.2015.09.014

DO - 10.1016/j.laa.2015.09.014

M3 - Article

SP - 242

EP - 259

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

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10.1016/j.laa.2015.09.014

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

Abstract

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All Science Journal Classification (ASJC) codes

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