A matrix approach for the semiclassical and coherent orthogonal polynomials

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

doi:10.1016/j.amc.2015.01.071

A matrix approach for the semiclassical and coherent orthogonal polynomials

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

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

11 Citations (Scopus)

Abstract

We obtain a matrix characterization of semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthogonal polynomials, and the lower triangular matrix that represents the orthogonal polynomials in terms of the monomial basis of polynomials. We also provide a matrix characterization for coherent pairs of linear functionals.

Original language	English
Pages (from-to)	459-471
Number of pages	13
Journal	Applied Mathematics and Computation
Volume	256
DOIs	https://doi.org/10.1016/j.amc.2015.01.071
Publication status	Published - 1 Apr 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.

Publisher Copyright:
© 2015 Elsevier Inc.

Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2015.01.071

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84922570218&origin=inward

Cite this

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doi = "10.1016/j.amc.2015.01.071",

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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. Publisher Copyright: © 2015 Elsevier Inc. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.

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N2 - We obtain a matrix characterization of semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthogonal polynomials, and the lower triangular matrix that represents the orthogonal polynomials in terms of the monomial basis of polynomials. We also provide a matrix characterization for coherent pairs of linear functionals.

AB - We obtain a matrix characterization of semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthogonal polynomials, and the lower triangular matrix that represents the orthogonal polynomials in terms of the monomial basis of polynomials. We also provide a matrix characterization for coherent pairs of linear functionals.

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A matrix approach for the semiclassical and coherent orthogonal polynomials

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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