We generalize the relationship between the classical moment problem and the spectral theory of Jacobi matrices. We present the solution of the two-dimensional half-strong moment problem and suggest an analog of Jacobi-type matrices associated with the two-dimensional half-strong moment problem and the corresponding system of polynomials orthogonal with respect to a measure with compact support in the real plane.

中文翻译：

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二维半强实矩问题和相应的块矩阵。第一部分

我们概括了经典矩问题与雅可比矩阵谱理论之间的关系。我们提出了二维半强矩问题的解决方案，并提出了与二维半强矩问题相关的 Jacobi 型矩阵的模拟，以及相对于具有紧凑支持的测度正交的相应多项式系统真正的飞机。