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The complex moment problem and subnormality: A polar decomposition approach

机译：复矩问题和超自然现象：一种极分解法

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It has been known that positive definiteness does not guarantee a bisequence to be a complex moment. However, it turns out that positive definite extendibility does (Theorems 1 and 22). and this is the main theme of this paper. The main tool is, generally understood, polar decomposition. To strengthen applicability of our approach we work out a criterion for positive definite extendibility in a fairly wide context (Theorems 9 and 29). All this enables us to prove characterizations of subnormality of unbounded operators having invariant domain (Theorems 37 and 39) and their further applications (Theorems 41 and 43) and a description of the complex moment problem on real algebraic curves (Theorems 52 and 56). The latter question is completed in the Appendix, in which we relate the complex moment problem to the two-dimensional real one, with emphasis on real algebraic sets. (C) 1998 Academic Press. [References: 50]
机译：众所周知，正定性并不能保证双序列是一个复杂的时刻。然而，事实证明，肯定的可扩展性确实存在（定理1和22）。这是本文的主题。通常理解，主要工具是极性分解。为了加强我们方法的适用性，我们制定了一个在相当宽泛的背景下确定正可扩展性的准则（定理9和29）。所有这些使我们能够证明具有不变域的无界算子（定理37和39）及其进一步应用（定理41和43）的次正规性的刻画以及对实数代数曲线上复矩问题的描述（定理52和56）。后一个问题在附录中完成，其中我们将复矩问题与二维实数问题联系起来，重点是实数代数集。 （C）1998年学术出版社。 [参考：50]

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