Abstract
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) nj=0 is obtained in a general case, when the block Hankel matrix Γn ≔ (Cj+k) nj,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.
To Heinz Langer with admiration and gratitude for fruitful co-operation
The authors appreciate the fair work and helpful suggestions and corrections of the referees of this paper.
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Adamyan, V.M., Tkachenko, I.M. (2005). General Solution of the Stieltjes Truncated Matrix Moment Problem. In: Langer, M., Luger, A., Woracek, H. (eds) Operator Theory and Indefinite Inner Product Spaces. Operator Theory: Advances and Applications, vol 163. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7516-7_1
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