Opuscula Mathematica

Opuscula Math.
 25
, no. 1
 (), 5-24
Opuscula Mathematica

Solution of the Stieltjes truncated matrix moment problem



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.
Mathematics Subject Classification: 30E05, 30E10.
Cite this article as:
Vadim M. Adamyan, Igor M. Tkachenko, Solution of the Stieltjes truncated matrix moment problem, Opuscula Math. 25, no. 1 (2005), 5-24
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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