论文标题
关于特征功能的功能的注释
A note on powers of the characteristic function
论文作者
论文摘要
令$ ch（r）$表示实际行$ r $上的概率度量（分布）特征功能的家族。我们研究以下问题：鉴于整数$ n> 1 $，是否存在两个不同的$ f，g \ in ch（r）$中的$ f^n \ equiv g^n $？对于正面的$ n $，众所周知的例子以肯定的方式回答了这个问题。事实证明，对于任何奇数$ n> 1 $也是如此。对于$ f \ in Ch（r）$和Integer $ n> 1 $，设置$ c_n（f）= \ {g \ in ch（r）：g^n \ equiv f^n \} $。在本文中，我们对$ C_N（F）$的基数（或红衣主教号）估算。此外，我们描述了我们的估计量很高的$ f $。
Let $CH(R)$ denote the family of characteristic functions of probability measures (distributions) on the real line $R$. We study the following question: given an integer $n>1$, do there exist two different $f, g\in CH(R)$ such that $ f^n\equiv g^n$? For positive even $n$, well-known examples answer this question in the affirmative. It turns out that the same is true also for any odd $n>1$. For $f\in CH(R)$ and integer $n>1$, set $C_n(f)=\{g\in CH(R): g^n\equiv f^n\}$. In this paper, we give an estimate for cardinality (or cardinal number) of $C_n(f)$. In addition, we describe such $f$ for which our estimate is sharp.
