Devinatz's moment problem: a description of all solutions

Abstract

In this paper we study Devinatz's moment problem: to find a non-negative Borel measure $\mu$ in a strip $\Pi =\{(x,\varphi ):x\in \mathbb{R},-\pi \le \varphi <\pi \},$ such that ${\int }_{\Pi }{x}^m{e}^{in\varphi }d\mu =s_{m,n}$, $m\in {\mathbb{Z}}_{+}$, $n\in \mathbb{Z}$, 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 Godič, Lucenko and Shtraus.

26 pages

Cited by in corpus (1)

• On the density of polynomials in some $L^2(M)$ spaces