论文标题
非阴性形式，巨大的集合，完整的单调性和力矩矩阵
Non-negative forms, volumes of sublevel sets, complete monotonicity and moment matrices
论文作者
论文摘要
令$ \ MATHCAL {C} _ {D，N} $为凸锥，由实际$ n $ - 比度$ d $ forms组成，这些$ d $表格严格呈$ \ m athbb {r}^n \ setMinus \ {\ setMinus \ {\ setMinus \ {\ mathbf {\ mathbf {0} \} $。我们证明，$ g \ in \ Mathcal {c} _ {d，n} $的$ g \ $ g \ $ g \ of sublevel set的lebesgue音量是$ \ nathcal {c} _ {c} _ {d，n} $上的完全单调函数。此外，我们提供（部分）表格的表征，其级别的集合具有有限的lebesgue量。最后，我们发现了一个中心的高斯分布的有趣属性，建立了其$ d $矩的矩阵与其协方差矩阵倒数的二次形式之间的联系。
Let $\mathcal{C}_{d,n}$ be the convex cone consisting of real $n$-variate degree $d$ forms that are strictly positive on $\mathbb{R}^n\setminus \{\mathbf{0}\}$. We prove that the Lebesgue volume of the sublevel set $\{g\leq 1\}$ of $g\in \mathcal{C}_{d,n}$ is a completely monotone function on $\mathcal{C}_{d,n}$ and investigate the related properties. Furthermore, we provide (partial) characterization of forms, whose sublevel sets have finite Lebesgue volume. Finally, we discover an interesting property of a centered Gaussian distribution, establishing a connection between the matrix of its degree $d$ moments and the quadratic form given by the inverse of its covariance matrix.
