Matrix Uvarov Transformation on the Unit Circle: Asymptotic Properties

Herbert Dueñas; Edinson Fuentes; Luis E. Garza

doi:10.1007/s40840-020-00947-2

Matrix Uvarov Transformation on the Unit Circle: Asymptotic Properties

Herbert Dueñas, Edinson Fuentes, Luis E. Garza^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

Let σ be an l× l Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of matrix orthogonal polynomials associated with the Uvarov matrix transformation of σ defined by dσum(z)=dσ(z)+∑j=1mMjδ(z-ζj),where M_j is an l× l positive definite matrix, ζ_j∈ C with ζ_j≠ ζ_i and δ is the Dirac matrix measure.

Original language	English
Pages (from-to)	279-315
Number of pages	37
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	44
Issue number	1
DOIs	https://doi.org/10.1007/s40840-020-00947-2
Publication status	Published - Jan 2021
Externally published	Yes

Bibliographical note

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© 2020, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s40840-020-00947-2

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abstract = "Let σ be an l× l Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of matrix orthogonal polynomials associated with the Uvarov matrix transformation of σ defined by dσum(z)=dσ(z)+∑j=1mMjδ(z-ζj),where Mj is an l× l positive definite matrix, ζj∈ C with ζj≠ ζi and δ is the Dirac matrix measure.",

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AB - Let σ be an l× l Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of matrix orthogonal polynomials associated with the Uvarov matrix transformation of σ defined by dσum(z)=dσ(z)+∑j=1mMjδ(z-ζj),where Mj is an l× l positive definite matrix, ζj∈ C with ζj≠ ζi and δ is the Dirac matrix measure.

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Matrix Uvarov Transformation on the Unit Circle: Asymptotic Properties

Abstract

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