### Abstract

^{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 |
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Pages (from-to) | 242-259 |

Number of pages | 18 |

Journal | Linear Algebra and Its Applications |

DOIs | |

Publication status | Published - 15 Dec 2015 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Linear Algebra and Its Applications*, 242-259. https://doi.org/10.1016/j.laa.2015.09.014

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*Linear Algebra and Its Applications*, pp. 242-259. https://doi.org/10.1016/j.laa.2015.09.014

**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.

Research output: Contribution to journal › Article

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

SP - 242

EP - 259

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -