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Zbl 1210.44005
Zagorodnyuk, S.
On the two-dimensional moment problem.
(English)
[J] Ann. Funct. Anal. AFA 1, No. 1, 80-104, electronic only (2010). ISSN 2008-8752/e

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.
[Osman Yürekli (Ithaca)]
MSC 2000:
*44A60 Moment problems
30E05 Moment problems, etc.

Keywords: two-dimensional moment problem; quasi-Hilbert space; algorithm; complex moment problem

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