On the truncated operator trigonometric moment problem
Sergey M. Zagorodnyuk
TL;DR
This paper investigates the truncated operator trigonometric moment problem, providing a comprehensive description of all solutions via a Nevanlinna-type parameterization and establishing conditions for problem determinacy.
Contribution
It introduces a Nevanlinna-type parameterization for all solutions and computes operator coefficient matrices from prescribed moments in separable Hilbert spaces.
Findings
All solutions described by Nevanlinna-type parameterization
Operator coefficient matrices explicitly calculated
Conditions for determinacy established
Abstract
In this paper we study the truncated operator trigonometric moment problem. All solutions of the moment problem are described by a Nevanlinna-type parameterization. In the case of moments acting in a separable Hilbert space, the matrices of the operator coefficients in the Nevanlinna-type formula are calculated by the prescribed moments. Conditions for the determinacy of the moment problem are given, as well.
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