On Positive Definiteness of Some Functions
Let [rho] be a nonnegative homogeneous function on n. General structure of the set of numerical pairs ([delta],Â [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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 73 (2000)
Issue (Month): 1 (April)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Richards, Donald St. P., 1985. "Positive definite symmetric functions on finite-dimensional spaces II," Statistics & Probability Letters, Elsevier, vol. 3(6), pages 325-329, October.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:73:y:2000:i:1:p:55-81. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If references are entirely missing, you can add them using this form.