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 journalArticlepeer-review

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+〈pM1,qM2u1, where M1 and M2 are m×m non-singular matrices and p,q are matrix polynomials.

Original languageEnglish
Article number126674
JournalJournal of Mathematical Analysis and Applications
Volume518
Issue number1
DOIs
Publication statusPublished - 1 Feb 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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