Riesz's theorem for orthogonal matrix polynomials

Abstract

We describe the image through the Stieltjes transform of the set of solutions V of a matrix moment problem. We extend Riesz's theorem to the matrix setting, proving that those matrices of measures of V for which the matrix polynomials are dense in the corresponding L2 space are precisely those whose Stieltjes transform is an extremal point (in the sense of convexity) of the image set.