On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures

Abstract

In this paper, we prove that any sequence of polynomials ( p n ) n for which dgr( p n ) = n which satisfies a (2 N + l)-term recurrence relation is orthogonal with respect to a positive definite N × N matrix of measures. We use that result to prove asymptotic properties of the kernel polynomials associated to a positive measure or a positive definite matrix of measures. Finally, some examples are given.