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A Notion of Positive Definiteness for Arithmetical Functions

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Details

Original languageEnglish
Title of host publicationMatrices, Statistics and Big Data
Subtitle of host publicationSelected Contributions from IWMS 2016
EditorsS. Ejaz Ahmed, Francisco Carvalho, Simo Puntanen
PublisherSpringer Nature
Pages61-74
Number of pages14
ISBN (Electronic)978-3-030-17519-1
ISBN (Print)978-3-030-17518-4
DOIs
Publication statusPublished - 2019
Publication typeA4 Article in a conference publication
EventInternational Workshop on Matrices and Statistics - Funchal, Portugal
Duration: 6 Jun 20169 Jun 2016
Conference number: 25

Publication series

NameContributions to Statistics
ISSN (Print)1431-1968

Conference

ConferenceInternational Workshop on Matrices and Statistics
Abbreviated titleIWMS
CountryPortugal
CityFunchal
Period6/06/169/06/16

Abstract

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.

Publication forum classification

Field of science, Statistics Finland