Opuscula Math. 25, no. 1 (2005), 5-24
Opuscula Mathematica
Solution of the Stieltjes truncated matrix moment problem
Vadim M. Adamyan
Igor M. Tkachenko
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.
- Vadim M. Adamyan
- I. I. Mechnikov Odessa National University, Department of Theoretical Physics, 65026 Odessa, Ukraine
- Igor M. Tkachenko
- Polytechnic University of Valencia, Department of Applied Mathematics, 46022 Valencia, Spain
- Received: 2004-09-17.
