论文标题
Kagan在Banach空间上的定理
The Kagan characterization theorem on Banach spaces
论文作者
论文摘要
A. Kagan引入了分布类$ \ MATHCAL {D} _ {M，K} $中的$ M $ -Dimensional Space $ \ Mathbb {R}^M $。他证明，如果$ n $ n $独立变量的$ m $线性形式的联合分布属于$ \ mathcal {d} _ {m，m-1} $类，则随机变量是高斯。如果$ m = 2 $，则Kagan定理意味着众所周知的Darmois-Skitovich定理，其中高斯分布的特征在于$ n $独立的随机变量的两种线性形式的独立性。在论文中，我们描述了Banach空间，其中Kagan定理的类似物是有效的。
A. Kagan introduced classes of distributions $\mathcal{D}_{m,k}$ in $m$-dimensional space $\mathbb{R}^m$. He proved that if the joint distribution of $m$ linear forms of $n$ independent random variables belong to the class $\mathcal{D}_{m,m-1}$ then the random variables are Gaussian. If $m=2$ then the Kagan theorem implies the well-known Darmois-Skitovich theorem, where the Gaussian distribution is characterized by the independence of two linear forms of $n$ independent random variables. In the paper we describe Banach spaces where the analogue of the Kagan theorem is valid.
