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.