In this paper we study Devinatz's moment problem: to find a non-negative Borel measure $\mu$ in a strip $\Pi = \{ (x,\phi):\ x\in \mathbb{ R},\ -\pi\leq \phi < \pi\},$ such that $\int_\Pi x^m e^{ in\phi} d\mu = s_{ m,n}$, $m\in \mathbb{ Z}_+$, $n\in \mathbb{ Z}$, 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 Godi\v{ c}, Lucenko and Shtraus.
Categories: math.FA