A Notion of Positive Definiteness for Arithmetical Functions

Autor:	Mika Mattila, Pentti Haukkanen
Přispěvatelé:	Ahmed, S. Ejaz, Carvalho, Francisco, Puntanen, Simo, Informaatioteknologian ja viestinnän tiedekunta - Faculty of Information Technology and Communication Sciences, Tampere University
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Class (set theory) Pure mathematics Property (philosophy) Tilastotiede - Statistics and probability Positive-definite function Positive definiteness Matematiikka - Mathematics Arithmetic function Partially ordered set Domain (mathematical analysis) Mathematics Real number
Zdroj:	Contributions to Statistics ISBN: 9783030175184
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::42680b0fc13438066b6bdd566029c9b0 https://trepo.tuni.fi/handle/10024/117105 Zobrazit plný text záznamu