The two-dimensional moment problem in a strip

TL;DR

This paper investigates the two-dimensional moment problem within a strip, providing a solvability criterion and a complete parameterization of all solutions using an operator-theoretic approach.

Contribution

It introduces a solvability criterion and a full solution parameterization for the two-dimensional moment problem in a strip, extending existing methods.

Findings

Established a solvability criterion for the problem

Derived a parameterization of all solutions

Utilized an abstract operator approach

Abstract

In this paper we study the two-dimensional moment problem in a strip $\Pi(R) = \{ (x_1,x_2)\in \mathbb{R}^2:\ |x_2| \leq R \}$, $R>0$. We obtained a solvability criterion for this moment problem. We derived a parameterization of all solutions of the moment problem. An abstract operator approach and results of Godi\v{c}, Lucenko and Shtraus are used.