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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 μ in 2 such that

2 x 1 m x 2 n dμ=s m,n ,m,n +

where {s m,n } m,n + 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.

MSC:
44A60Moment problems (integral transforms)
30E05Moment problems, interpolation problems