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A Note on n-Divisible Positive Definite Functions

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  • Saulius Norvidas
  • Firdous A. Shah

Abstract

Let PD℠be the family of continuous positive definite functions on ℠. For an integer n>1, a f∈PD℠is called n-divisible if there is g∈PD℠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∈PD℠: gn=f for n-divisible f∈PD℠and obtain precise estimate for the cardinality of this class.

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  • Saulius Norvidas & Firdous A. Shah, 2022. "A Note on n-Divisible Positive Definite Functions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, November.
    • Handle: RePEc:hin:jjmath:9419427
    DOI: 10.1155/2022/9419427
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