A Note on n-Divisible Positive Definite Functions
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 intege...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9419427 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2314-4785 |