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A Note on n‐Divisible Positive Definite Functions

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  • Saulius Norvidas

Abstract

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

Suggested Citation

  • Saulius Norvidas, 2022. "A Note on n‐Divisible Positive Definite Functions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:9419427
    DOI: 10.1155/2022/9419427
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    References listed on IDEAS

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    1. Roald M. Trigub & Eduard S. Bellinsky, 2004. "Fourier Analysis and Approximation of Functions," Springer Books, Springer, number 978-1-4020-2876-2, January.
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