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- W3083244559 abstract "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 $f, gin CH(R)$ such that $ f^nequiv 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 $fin CH(R)$ and integer $n>1$, set $C_n(f)={gin CH(R): g^nequiv f^n}$. 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." @default.
- W3083244559 created "2020-09-11" @default.
- W3083244559 creator A5034695570 @default.
- W3083244559 date "2020-09-06" @default.
- W3083244559 modified "2023-09-27" @default.
- W3083244559 title "A note on powers of the characteristic function" @default.
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