A Notion of Positive Definiteness for Arithmetical Functions
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Yksityiskohdat
| Alkuperäiskieli | Englanti |
|---|---|
| Otsikko | Matrices, Statistics and Big Data |
| Alaotsikko | Selected Contributions from IWMS 2016 |
| Toimittajat | S. Ejaz Ahmed, Francisco Carvalho, Simo Puntanen |
| Kustantaja | Springer Nature |
| Sivut | 61-74 |
| Sivumäärä | 14 |
| ISBN (elektroninen) | 978-3-030-17519-1 |
| ISBN (painettu) | 978-3-030-17518-4 |
| DOI - pysyväislinkit | |
| Tila | Julkaistu - 2019 |
| OKM-julkaisutyyppi | A4 Artikkeli konferenssijulkaisussa |
| Tapahtuma | International Workshop on Matrices and Statistics - Funchal, Portugali Kesto: 6 kesäkuuta 2016 → 9 kesäkuuta 2016 Konferenssinumero: 25 |
Julkaisusarja
| Nimi | Contributions to Statistics |
|---|---|
| ISSN (painettu) | 1431-1968 |
Conference
| Conference | International Workshop on Matrices and Statistics |
|---|---|
| Lyhennettä | IWMS |
| Maa | Portugali |
| Kaupunki | Funchal |
| Ajanjakso | 6/06/16 → 9/06/16 |
Tiivistelmä
In the theory of Fourier transform some functions are said to be positive definite based on the positive definiteness property of a certain class of matrices associated with these functions. In the present article we consider how to define a similar positive definiteness property for arithmetical functions, whose domain is not the set of real numbers but merely the set of positive integers. After finding a suitable definition for this concept we shall use it to construct a partial ordering on the set of arithmetical functions. We shall study some of the basic properties of our newly defined relations and consider a couple of well-known arithmetical functions as examples.