1. CMB 2009 (vol 52 pp. 95)
|Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory |
In the work presented below the classical subject of orthogonal polynomials on the unit circle is discussed in the matrix setting. An explicit matrix representation of the matrix valued orthogonal polynomials in terms of the moments of the measure is presented. Classical recurrence relations are revisited using the matrix representation of the polynomials. The matrix expressions for the kernel polynomials and the Christoffel--Darboux formulas are presented for the first time.
Keywords:Matrix valued orthogonal polynomials, unit circle, Schur complements, recurrence relations, kernel polynomials, Christoffel-Darboux