@Article{Adamyan2005,
author = "Adamyan, Vadim M. and Tkachenko, Igor M.",
title = "Solution of the Stieltjes truncated matrix moment problem",
journal = "Opuscula Math.",
year = "2005",
volume = "25",
number = "1",
pages = "5--24",
doi = "http://dx.doi.org/10.7494/OpMath.2005.25.1.5",
url = "http://dx.doi.org/10.7494/OpMath.2005.25.1.5",
abstract = "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.",
keywords = "Stieltjes power moments, canonical solutions, Nevanlinna's formula",
issn = "1232-9274"
}