同矩构造措施
Constructing measures with identical moments
摘要：
Nevanlinna参数化建立了具有指定矩集的所有测度的类与Pick函数的类之间的双射。所有通过Nevanlinna参数化构造的测度都具有相同的矩，这一事实来自于正交多项式和连分数理论。在本文中，我们探索相反的方向：我们构造一组措施，我们表明，他们都有相同的时刻，然后我们建立一个Nevanlinna型参数化这组措施。我们的构造不需要正交多项式的理论，它揭示了Nevanlinna参数化背后的分析结构。
英文摘要：
The Nevanlinna parametrization establishes a bijection between the class of all measures having a prescribed set of moments and the class of Pick functions. The fact that all measures constructed through the Nevanlinna parametrization have identical moments follows from the theory of orthogonal polynomials and continued fractions. In this paper we explore the opposite direction: we construct a set of measures and we show that they all have identical moments, and then we establish a Nevanlinna-type parametrization for this set of measures. Our construction does not require the theory of orthogonal polynomials and it exposes the analytic structure behind the Nevanlinna parametrization.
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