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On the two-dimensional moment problem. (English) Zbl 1210.44005
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.
44A60Moment problems (integral transforms)
30E05Moment problems, interpolation problems
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