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 journalArticlepeer-review

2 Citations (Scopus)


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
Publication statusPublished - 15 Dec 2015
Externally publishedYes

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 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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