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

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

Research output: Contribution to journalArticle

Abstract

© 2015 Elsevier Inc. All rights reserved. We present a new structure relation for the sequence of orthogonal polynomials associated with a -semiclassical linear functional of class s, and then we use it to obtain a matrix characterization of the -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 -coherent pairs of linear functionals.
Original languageEnglish
Pages (from-to)242-259
Number of pages18
JournalLinear Algebra and Its Applications
DOIs
Publication statusPublished - 15 Dec 2015
Externally publishedYes

Fingerprint

Orthogonal Polynomials
Semiclassical Orthogonal Polynomials
Polynomials
Lower triangular matrix
Orthonormal Polynomials
Multiplication Operator
Jacobi Matrix
Linear Functionals
Linear Functional
Polynomial
Mathematical operators
Class

All Science Journal Classification (ASJC) codes

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

Cite this

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abstract = "{\circledC} 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.",
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A matrix characterization for the <sup>Dν</sup>-semiclassical and <sup>Dν</sup>-coherent orthogonal polynomials. / Garza, Lino G.; Garza, Luis E.; Marcellán, Francisco; Pinzón-Cortés, Natalia C.

In: Linear Algebra and Its Applications, 15.12.2015, p. 242-259.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A matrix characterization for the Dν-semiclassical and Dν-coherent orthogonal polynomials

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

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EP - 259

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

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