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Orthogonal Matrix Polynomials, Connection Between Recurrences on the Unit Circle and on a Finite Interval

  • Hossain O. Yakhlef
  • Francisco Marcellán

Abstract

Orthogonal matrix polynomials on the unit circle and on a finite interval are completely determined by their reflection matrix parameters through the Szegő recurrences and by their matrix coefficients through the three-term recurrence relation, respectively. The aim of this paper is to study a connection between those matrix recurrence coefficients and to deduce relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on a finite interval.

Keywords

Unit Circle Positive Definite Matrix Matrix Measure Matrix Polynomial Relative Asymptotics 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Hossain O. Yakhlef
    • 1
  • Francisco Marcellán
    • 2
  1. 1.Departamento de Matemática AplicadaUniversidad de GranadaGranadaSpain
  2. 2.Departamento de MatemáticasUniversidad Carlos III de MadridLeganésSpain

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