The matrix Stieltjes moment problem: a description of all solutions
Sergey M. Zagorodnyuk
TL;DR
This paper provides a comprehensive description of all solutions to the matrix Stieltjes moment problem without additional conditions, utilizing Krein's formula for generalized resolvents.
Contribution
It introduces a complete characterization of solutions to the matrix Stieltjes moment problem using Krein's formula, extending previous partial results.
Findings
All solutions are described explicitly.
The approach applies Krein's formula for generalized resolvents.
The results hold in the general solvable case.
Abstract
We describe all solutions of the matrix Stieltjes moment problem in the general case (no conditions besides solvability are assumed). We use Krein's formula for the generalized -resolvents of positive Hermitian operators in the form of V.A Derkach and M.M. Malamud.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Matrix Theory and Algorithms · Quantum Mechanics and Non-Hermitian Physics