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 \( {\cal L} \) 2 space are precisely those whose Stieltjes transform is an extremal point (in the sense of convexity) of the image set.
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May 20, 1997. Date revised: January 8, 1998.
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López-Rodríguez, P. Riesz's Theorem for Orthogonal Matrix Polynomials. Constr. Approx. 15, 135–151 (1999). https://doi.org/10.1007/s003659900101
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DOI: https://doi.org/10.1007/s003659900101