On a class of matrix orthogonal polynomials on the real line

AbstractIt is shown how to construct matrix orthogonal polynomials on the real line provided we have a sequence of scalar orthogonal polynomials over an algebraic harmonic curve Γ. We consider the moment matrix associated with a distribution on Γ and related to a basis of the linear space of polynomials, obtained through the polynomial which defines the curve. This particular moment matrix can be regarded as a Hankel block matrix, and thus matrix orthogonal polynomials appear in a natural way