Coherent pairs and Sobolev-type orthogonal polynomials on the real line: An extension to the matrix case

Edinson Fuentes; Luis E. Garza

doi:10.1016/j.jmaa.2022.126674

Coherent pairs and Sobolev-type orthogonal polynomials on the real line: An extension to the matrix case

Edinson Fuentes, Luis E. Garza^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

In this contribution, we extend the concept of coherent pair for two quasi-definite matrix linear functionals u₀ and u₁. Necessary and sufficient conditions for these functionals to constitute a coherent pair are determined, when one of them satisfies a matrix Pearson-type equation. Moreover, we deduce algebraic properties of the matrix orthogonal polynomials associated with the Sobolev-type inner product 〈p,q〉_s=〈p,q〉_u₀+〈p^′M₁,q^′M₂〉_u₁, where M₁ and M₂ are m×m non-singular matrices and p,q are matrix polynomials.

Original language	English
Article number	126674
Journal	Journal of Mathematical Analysis and Applications
Volume	518
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2022.126674
Publication status	Published - 1 Feb 2023
Externally published	Yes

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© 2022 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jmaa.2022.126674

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abstract = "In this contribution, we extend the concept of coherent pair for two quasi-definite matrix linear functionals u0 and u1. Necessary and sufficient conditions for these functionals to constitute a coherent pair are determined, when one of them satisfies a matrix Pearson-type equation. Moreover, we deduce algebraic properties of the matrix orthogonal polynomials associated with the Sobolev-type inner product 〈p,q〉s=〈p,q〉u0+〈p′M1,q′M2〉u1, where M1 and M2 are m×m non-singular matrices and p,q are matrix polynomials.",

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AB - In this contribution, we extend the concept of coherent pair for two quasi-definite matrix linear functionals u0 and u1. Necessary and sufficient conditions for these functionals to constitute a coherent pair are determined, when one of them satisfies a matrix Pearson-type equation. Moreover, we deduce algebraic properties of the matrix orthogonal polynomials associated with the Sobolev-type inner product 〈p,q〉s=〈p,q〉u0+〈p′M1,q′M2〉u1, where M1 and M2 are m×m non-singular matrices and p,q are matrix polynomials.

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Coherent pairs and Sobolev-type orthogonal polynomials on the real line: An extension to the matrix case

Abstract

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