A canonical Geronimus transformation for matrix orthogonal polynomials

Juan Carlos García-Ardila; Luis E. Garza; Francisco Marcellán

doi:10.1080/03081087.2017.1299089

A canonical Geronimus transformation for matrix orthogonal polynomials

Juan Carlos García-Ardila, Luis E. Garza^*, Francisco Marcellán

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

We consider matrix polynomials orthogonal with respect to a sesquilinear form (Formula presented.) such that (Formula presented.) where µ is a symmetric, positive definite matrix of measures supported in some infinite subset J of the real line, and W(t) is a matrix polynomial of degree 1. We obtain a connection formula between the sequences of matrix polynomials orthogonal with respect to [·, ·]W and µ, as well as a relation between the corresponding block Jacobi matrices. A non-symmetric sesquilinear form is also considered.

Original language	English
Pages (from-to)	357-381
Number of pages	25
Journal	Linear and Multilinear Algebra
Volume	66
Issue number	2
DOIs	https://doi.org/10.1080/03081087.2017.1299089
Publication status	Published - 1 Feb 2018
Externally published	Yes

Bibliographical note

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© 2017 Informa UK Limited, trading as Taylor & Francis Group.

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1080/03081087.2017.1299089

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AU - Garza, Luis E.

AU - Marcellán, Francisco

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N2 - We consider matrix polynomials orthogonal with respect to a sesquilinear form (Formula presented.) such that (Formula presented.) where µ is a symmetric, positive definite matrix of measures supported in some infinite subset J of the real line, and W(t) is a matrix polynomial of degree 1. We obtain a connection formula between the sequences of matrix polynomials orthogonal with respect to [·, ·]W and µ, as well as a relation between the corresponding block Jacobi matrices. A non-symmetric sesquilinear form is also considered.

AB - We consider matrix polynomials orthogonal with respect to a sesquilinear form (Formula presented.) such that (Formula presented.) where µ is a symmetric, positive definite matrix of measures supported in some infinite subset J of the real line, and W(t) is a matrix polynomial of degree 1. We obtain a connection formula between the sequences of matrix polynomials orthogonal with respect to [·, ·]W and µ, as well as a relation between the corresponding block Jacobi matrices. A non-symmetric sesquilinear form is also considered.

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ER -

A canonical Geronimus transformation for matrix orthogonal polynomials

Abstract

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