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- W4304194101 abstract "Let $PD(mathbb{R})$ be the family of continuous positive definite functions on $mathbb{R}$. For an integer $n>1$, a $fin PD(mathbb{R})$ is called $n$-divisible if there is $gin PD(mathbb{R})$ 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 ${gin PD(mathbb{R}): g^n=f}$ for $n$-divisible $fin PD(mathbb{R})$ and obtain precise estimate for the cardinality of this class." @default.
- W4304194101 created "2022-10-11" @default.
- W4304194101 creator A5034695570 @default.
- W4304194101 date "2022-09-25" @default.
- W4304194101 modified "2023-09-24" @default.
- W4304194101 title "A note on n-divisible positive definite functions" @default.
- W4304194101 doi "https://doi.org/10.48550/arxiv.2210.03503" @default.
- W4304194101 hasPublicationYear "2022" @default.
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