Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory

Miranian, L.

Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 95-104

Résumé

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.

Détail

DOI : 10.4153/CMB-2009-012-3

Mots-clés : 42C99, Matrix valued orthogonal polynomials, unit circle, Schur complements, recurrence relations, kernel polynomials, Christoffel-Darboux

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