Density questions for the truncated matrix moment problem

http://dx.doi.org/10.4153/CJM-1997-034-5
Canad. J. Math. 49(1997), 708-721

  Published:1997-08-01
 Printed: Aug 1997

For a truncated matrix moment problem, we describe in detail the set of positive definite matrices of measures $\mu$ in $V_{2n}$ (this is the set of solutions of the problem of degree $2n$) for which the polynomials up to degree $n$ are dense in the corresponding space ${\cal L}^2(\mu)$. These matrices of measures are exactly the extremal measures of the set $V_n$.