TY  - JOUR
ID  - Adamyan2005
LB  - Adamyan2005
AU  - Adamyan, Vadim M.
AU  - Tkachenko, Igor M.
TI  - Solution of the Stieltjes truncated matrix moment problem
ST  - Solution of the Stieltjes truncated matrix moment problem
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2005
VL  - 25
IS  - 1
SP  - 5
EP  - 24
DO  - http://dx.doi.org/10.7494/OpMath.2005.25.1.5
UR  - http://dx.doi.org/10.7494/OpMath.2005.25.1.5
AB  - The truncated Stieltjes matrix moment problem consisting in the description of all matrix distributions \(\boldsymbol{\sigma}(t)\) on \([0,\infty)\) with given first \(2n+1\) power moments \((\mathbf{C}_j)_{n=0}^j\) is solved using known results on the corresponding Hamburger problem for which \(\boldsymbol{\sigma}(t)\) are defined on \((-\infty,\infty)\). The criterion of solvability of the Stieltjes problem is given and all its solutions in the non-degenerate case are described by selection of the appropriate solutions among those of the Hamburger problem for the same set of moments. The results on extensions of non-negative operators are used and a purely algebraic algorithm for the solution of both Hamburger and Stieltjes problems is proposed.
KW  - Stieltjes power moments
KW  - canonical solutions
KW  - Nevanlinna's formula
SN  - 1232-9274
ER  -