概率子集上的全矩问题与点构形
The full moment problem on subsets of probabilities and point configurations
摘要：
本文研究了无穷维向量空间中某些特殊非线性子集$K$上测度的全$K-$矩问题.我们重点关注随机测量的情况，即$K$是$\mathbb{R}^d$上所有非负Radon测量的子集。我们认为$K$的子概率，概率和点配置的空间$\mathbb{R}^d$。对于这些空间中的每一个，我们提供至少一个表示为广义基本闭半代数集，以应用[J. Funct.肛门，267（2014）no.5：1382- 1418]。我们证明，这一主要结果可以显着改善进一步考虑的基础上，特别选择的$K$的表示。在$K$是点构形空间的情况下，相关函数（也称为阶乘矩函数）比普通矩函数更容易处理。因此，我们另外表示的相关函数的主要结果。
英文摘要：
The aim of this paper is to study the full $K-$moment problem for measures supported on some particular non-linear subsets $K$ of an infinite dimensional vector space. We focus on the case of random measures, that is $K$ is a subset of all non-negative Radon measures on $\mathbb{R}^d$. We consider as $K$ the space of sub-probabilities, probabilities and point configurations on $\mathbb{R}^d$. For each of these spaces we provide at least one representation as a generalized basic closed semi-algebraic set to apply the main result in [J. Funct. Anal., 267 (2014) no.5: 1382--1418]. We demonstrate that this main result can be significantly improved by further considerations based on the particular chosen representation of $K$. In the case when $K$ is a space of point configurations, the correlation functions (also known as factorial moment functions) are easier to handle than the ordinary moment functions. Hence, we additionally express the main results in terms of correlation functions.
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