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...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9419427 |
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| author | Saulius Norvidas |
| author_facet | Saulius Norvidas |
| author_sort | Saulius Norvidas |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-10e50e384acf4accb0cdfb57230d0c57 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-10e50e384acf4accb0cdfb57230d0c572025-02-03T05:57:25ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9419427A Note on n-Divisible Positive Definite FunctionsSaulius Norvidas0Faculty of Mathematics and InformaticsLet 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.http://dx.doi.org/10.1155/2022/9419427 |
| spellingShingle | Saulius Norvidas A Note on n-Divisible Positive Definite Functions Journal of Mathematics |
| title | A Note on n-Divisible Positive Definite Functions |
| title_full | A Note on n-Divisible Positive Definite Functions |
| title_fullStr | A Note on n-Divisible Positive Definite Functions |
| title_full_unstemmed | A Note on n-Divisible Positive Definite Functions |
| title_short | A Note on n-Divisible Positive Definite Functions |
| title_sort | note on n divisible positive definite functions |
| url | http://dx.doi.org/10.1155/2022/9419427 |
| work_keys_str_mv | AT sauliusnorvidas anoteonndivisiblepositivedefinitefunctions AT sauliusnorvidas noteonndivisiblepositivedefinitefunctions |