General Solution of the Stieltjes Truncated Matrix Moment Problem
V. M. Adamyan, Igor M. Tkachenko · Birkhäuser Basel eBooks · 2005
The description of all solutions of the truncated Stieltjes matrix moment problem consisting in finding all s × s matrix measures dσ (t) on [0,∞) with given first 2n+1 power s×s matrix moments (Cj) =0 is obtained in a general case, when the block Hankel matrix Γn ≔ (Cj+k) =0 may be non-invertible. Special attention is paid to the description of canonical solutions for which dσ (t) is a sum of at most sn + s point matrix “masses” with the minimal sum of their ranks.