Journal of Operator Theory
Volume 68, Issue 2, Fall 2012 pp. 515-541.
Devinatz's moment problem: a description of all solutionsAuthors: Sergey M. Zagorodnyuk
Author institution: School of Mathematics and Mechanics, Karazin Kharkiv National University, Kharkiv, 61022, Ukraine
Summary: In this paper we study Devinatz's moment problem: to find a non-negative Borel measure μ in a strip Π={(x,φ): x∈R, −π⩽ such that \int\limits_\Pi x^m \mathrm{e}^{\mathrm{i}n\varphi} \mathrm 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 derive a solvability criterion for this moment problem. We obtain a parametrization of all solutions of Devinatz's moment problem. We use an abstract operator approach and results of Godi\v{c}, Lucenko and Shtraus.
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