论文标题
关于n可分别阳性确定功能的注释
A note on n-divisible positive definite functions
论文作者
论文摘要
令$ pd（\ mathbb {r}）$为$ \ mathbb {r} $的连续正定功能的家族。对于整数$ n> 1 $，如果pd（\ mathbb {r}）中有$ g \，则称为$ n $ -Divisible，a $ f \ in Pd（\ Mathbb {r}）$称为$ n $ -Divisible。无限分区和$ n $ - 可分布的功能的某些属性在本质上可能有所不同。的确，如果$ f $是无限的，那么对于每个整数$ n> 1 $，就有一个唯一的$ g $，因此$ g^n = f $，但是有一个$ n $ divisible $ f $，使得$ g^n = f $的因子$ g $通常不是唯一的。在本文中，我们讨论了Pd（\ Mathbb {r}）的类$ \ {g \ for $ n = f \} $的类别，$ n $ -divisible $ f \ in Pd（\ mathbb {r}）$中的$ n = f \} $，并获得此类持卡性的精确估计。
Let $PD(\mathbb{R})$ be the family of continuous positive definite functions on $\mathbb{R}$. For an integer $n>1$, a $f\in PD(\mathbb{R})$ is called $n$-divisible if there is $g\in PD(\mathbb{R})$ such that $g^n=f$. Some properties of infinite-divisible and $n$-divisible functions may differ in essence. Indeed, if $f$ is infinite-divisible, then for each integer $n>1$, there is an unique $g$ such that $g^n=f$, but there is a $n$-divisible $f$ such that the factor $g$ in $g^n=f$ is generally not unique. In this paper, we discuss about how rich can be the class $\{g\in PD(\mathbb{R}): g^n=f\}$ for $n$-divisible $f\in PD(\mathbb{R})$ and obtain precise estimate for the cardinality of this class.
