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

[摘要] In the work presented below the classical subject of orthogonalpolynomials on the unitcircle is discussed in the matrix setting. An explicit matrixrepresentation of the matrix valued orthogonal polynomials in terms ofthe moments of the measure is presented. Classical recurrencerelations are revisited using the matrix representation of thepolynomials. The matrix expressions for the kernel polynomials and theChristoffel--Darboux formulas are presented for the first time.

[学科分类] 数学（综合）

[关键词] Matrix valued orthogonal polynomials;unit circle;Schur complements;recurrence relations;kernel polynomials;Christoffel-Darboux