On Positive Definiteness of Some Functions

Victor P. Zastavnyi

Journal of Multivariate Analysis, 2000, vol. 73, issue 1, 55-81

Abstract: Let [rho] be a nonnegative homogeneous function on n. General structure of the set of numerical pairs ([delta], [lambda]), for which the function (1-[rho][lambda](x))[delta]+ is positive definite on n is investigated; a criterion for positive definiteness of this function is given in terms of completely monotonic functions; a connection of this problem with the Schoenberg problem on positive definiteness of the function exp(-[rho][lambda](x)) is found. We also obtain a general sufficient condition of Polya type for a function f([rho](x)) to be positive definite on n.

Keywords: positive definite; Schoenberg problems; Fourier transform; Bochner theorem; Lévy theorem; Hausdorff-Bernstein-Widder theorem. (search for similar items in EconPapers)
Date: 2000
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(99)91864-X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:73:y:2000:i:1:p:55-81

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().