On a Christoffel Transformation for Matrix Measures Supported on the Unit Circle

H. Dueñas; E. Fuentes; L. E. Garza

doi:10.1007/s40315-020-00324-x

On a Christoffel Transformation for Matrix Measures Supported on the Unit Circle

H. Dueñas, E. Fuentes, L. E. Garza^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

Let σ be a Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of the orthogonal matrix polynomials associated with the Christoffel matrix transformation of σ defined by dσcm(z)=Wm(z)Hdσ(z)Wm(z),where Wm(z)=∏j=1m(zI-Aj) and A_j is a square matrix for j= 1 , … , m. Moreover, we study the relative asymptotics of the associated orthogonal matrix polynomials when σcm satisfies a matrix condition in the diagonal case. Some illustrative examples are considered.

Original language	English
Pages (from-to)	219-243
Number of pages	25
Journal	Computational Methods and Function Theory
Volume	21
Issue number	2
DOIs	https://doi.org/10.1007/s40315-020-00324-x
Publication status	Published - Jun 2021
Externally published	Yes

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© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

All Science Journal Classification (ASJC) codes

Analysis
Computational Theory and Mathematics
Applied Mathematics

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abstract = "Let σ be a Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of the orthogonal matrix polynomials associated with the Christoffel matrix transformation of σ defined by dσcm(z)=Wm(z)Hdσ(z)Wm(z),where Wm(z)=∏j=1m(zI-Aj) and Aj is a square matrix for j= 1 , … , m. Moreover, we study the relative asymptotics of the associated orthogonal matrix polynomials when σcm satisfies a matrix condition in the diagonal case. Some illustrative examples are considered.",

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AU - Dueñas, H.

AU - Fuentes, E.

AU - Garza, L. E.

PY - 2021/6

Y1 - 2021/6

N2 - Let σ be a Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of the orthogonal matrix polynomials associated with the Christoffel matrix transformation of σ defined by dσcm(z)=Wm(z)Hdσ(z)Wm(z),where Wm(z)=∏j=1m(zI-Aj) and Aj is a square matrix for j= 1 , … , m. Moreover, we study the relative asymptotics of the associated orthogonal matrix polynomials when σcm satisfies a matrix condition in the diagonal case. Some illustrative examples are considered.

AB - Let σ be a Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of the orthogonal matrix polynomials associated with the Christoffel matrix transformation of σ defined by dσcm(z)=Wm(z)Hdσ(z)Wm(z),where Wm(z)=∏j=1m(zI-Aj) and Aj is a square matrix for j= 1 , … , m. Moreover, we study the relative asymptotics of the associated orthogonal matrix polynomials when σcm satisfies a matrix condition in the diagonal case. Some illustrative examples are considered.

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ER -

On a Christoffel Transformation for Matrix Measures Supported on the Unit Circle

Abstract

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