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arXiv · 1004.4087

Devinatz's moment problem: a description of all solutions

Sergey M. Zagorodnyuk
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Abstract

In this paper we study Devinatz's moment problem: to find a non-negative Borel measure $μ$ in a strip $Π= \{(x,ϕ):\ x\in \mathbb{R},\ -π\leq ϕ< π\},$ such that $\int_Πx^m e^{inϕ} dμ= s_{m,n}$, $m\in \mathbb{Z}_+$, $n\in \mathbb{Z}$, where $\{s_{m,n}\}_{m\in \mathbb{Z}_+, n\in \mathbb{Z}}$ is a given sequence of complex numbers. We present a new proof of the Devinatz solvability criterion for this moment problem. We obtained a parameterization of all solutions of Devinatz's moment problem. We used an abstract operator approach and results of Godič, Lucenko and Shtraus.

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Sergey M. Zagorodnyuk. 2010-04-23. Devinatz's moment problem: a description of all solutions. https://arxiv.org/abs/1004.4087

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