A Note on n-Divisible Positive Definite Functions - Saulius Norvidas (Journal of Mathematics)
Let PDℝ be the family of continuous positive definite functions on ℝ. For an integer n>1, a f∈PDℝ is called n-divisible if there is g∈PDℝ such that gn=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 gn=f, but there is a n-divisible f such that the factor g in gn=f is generally not unique. In this paper, we discuss about how rich can be the class g∈PDℝ: gn=f for n-divisible f∈PDℝ and obtain precise estimate for the cardinality of this class.