Orthogonal Matrix Polynomials, Connection Between Recurrences on the Unit Circle and on a Finite Interval
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.
KeywordsUnit Circle Positive Definite Matrix Matrix Measure Matrix Polynomial Relative Asymptotics
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