Let [Formula: see text], with [Formula: see text] and [Formula: see text], be a given complex-valued sequence. The complex moment problem (respectively, the general complex moment problem) associated with [Formula: see text] consists in determining necessary and sufficient conditions for the existence of a positive Borel measure (respectively, a charge) [Formula: see text] on [Formula: see text] such that [Formula: see text]In this paper, we investigate the notion of recursiveness in the two variable case. We obtain several useful results that we use to deduce new necessary and sufficient conditions for the truncated complex moment problem to admit a solution. In particular, we show that the general complex moment problem always has a solution. A concrete construction of the solution and an illustrating example are also given.

中文翻译：

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电荷解决截断复矩问题

令 [Formula: see text] 与 [Formula: see text] 和 [Formula: see text] 是给定的复值序列。与 [公式：见正文] 相关的复矩问题（分别为一般复矩问题）在于确定存在正 Borel 测度（分别为电荷）[公式：见正文] 的必要和充分条件。公式：见正文] 使得 [公式：见正文]在本文中，我们研究了两个变量情况下的递归概念。我们获得了几个有用的结果，我们使用这些结果来推导截断复矩问题的新的充分必要条件以允许解决方案。特别是，我们证明了一般复杂矩问题总是有解决方案的。还给出了解决方案的具体结构和示例。