On the two-dimensional moment problem (Q605413)

The two-dimensional moment problem consists of finding a non-negative Borel measure \(\mu\) in \({\mathbb R}^{2}\) such that \[ \int_{\mathbb R^{2}} x_{1}^{m}x_{2}^{n}\,d\mu=s_{m,n}, \quad m,n\in\mathbb Z_{+} \] where \(\{s_{m,n}\}_{m,n\in\mathbb Z_{+}}\) is prescribed sequence of complex numbers. The author obtains an algorithm to solve the two-dimensional moment problem. The algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. In addition, analogous results are obtained for the complex moment problem.