二维$L$ -矩量问题的极值解，II
Extremal solutions of the two-dimensional $L$-problem of moments, II
摘要：
在给定的紧集上，截断的$L$ -矩问题的所有极值解被描述为由一个多项式不等式给出的半代数集的特征函数.一个指数核，作为一个自然相关的亚正规算子与秩一自交换子的行列式函数，提供了一个自然的定义功能，这些半代数集。我们发现这个内核的一个内在的表征，我们描述了一系列的解析延拓性质，它是密切相关的行为的Schwarz反射函数的部分边界的极值支持集。
英文摘要：
All extremal solutions of the truncated $L$-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality. An exponential kernel, arising as the determinantal function of a naturally associated hyponormal operator with rank-one self-commutator, provides a natural defining function for these semi-algebraic sets. We find an intrinsic characterization of this kernel and we describe a series of analytic continuation properties of it which are closely related to the behaviour of the Schwarz reflection function in portions of the boundary of the extremal supporting set.
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