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Solution of the Stieltjes truncated matrix moment problem

Adamyan V.M., Tkachenko I.M.

Opuscula Mathematica

2005

Vol. 25, no. 1

5-24

The truncated Stieltjes matrix moment problem consisting in the description of all matrix distributions sigma(t) on [0, infin) with given first 2n + 1 power moments (Cj)nj=0 is solved using known results on the corresponding Hamburger problem for which sigma(t) are defined on (-infin, infin). 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.

Solution of the Stieltjes truncated moment problem

Adamyan V. M., Tkachenko I. M., Urrea M.

Journal of Applied Analysis

2003

Vol. 9, nr 1

57-74

The conditions of solvability and description of all solutions of the truncated Stieltjes moment problem are obtained using as the starting point earlier results on the Hamburger truncated moment problem. An algebraic algorithm for the explicit solution of both problems is proposed.

The Nevanlinna theorem of the classical theory of moments revisited

Urrea M., Tkachenko I. M., Fernández de Córdoba P.

Journal of Applied Analysis

2001

Vol. 7, nr 2

209-224

The canonical solutions of the truncated Hamburger moment problem (both in the classical and degenerate cases) are found. The Nevanlinna theorem which provides the noncanonical solutions of the truncated Hamburger problem is also rederived in the framework of the operator approach.