On the two-dimensional moment problem

TL;DR

This paper presents an algorithm that provides necessary and sufficient conditions for solving the two-dimensional moment problem, enabling the construction of all solutions and extending results to the complex moment problem.

Contribution

The paper introduces a new algorithm that fully characterizes the solvability of the two-dimensional moment problem and constructs all solutions, also applying to the complex case.

Findings

Algorithm determines solvability conditions

All solutions can be explicitly constructed

Results extend to complex moment problem

Abstract

In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. It is shown that all solutions of the moment problem can be constructed using this algorithm. In a consequence, analogous results are obtained for the complex moment problem.