Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

Extension of the Schoenberg theorem to integrally conditionally positive definite functions

Phillips, Tomos, Schmidt, Karl and Zhigljavsky, Anatoly 2019. Extension of the Schoenberg theorem to integrally conditionally positive definite functions. Journal of Mathematical Analysis and Applications 470 (1) , pp. 659-678. 10.1016/j.jmaa.2018.10.032
Item availability restricted.

[img] PDF (Updated version) - Accepted Post-Print Version
Restricted to Repository staff only until 11 October 2019 due to copyright restrictions.

Download (208kB)

Abstract

The celebrated Schoenberg theorem establishes a relation between positive definite and conditionally positive definite functions. In this paper, we consider the classes of real-valued functions P(J) and CP(J), which are positive definite and respectively, conditionally positive definite, with respect to a given class of test functions J. For suitably chosen J, the classes P(J) and CP(J) contain classically positive definite (respectively, conditionally positive definite) functions, as well as functions which are singular at the origin. The main result of the paper is a generalization of Schoenberg's theorem to such function classes.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Elsevier
ISSN: 0022-247X
Date of First Compliant Deposit: 12 October 2018
Date of Acceptance: 11 October 2018
Last Modified: 29 Apr 2019 10:33
URI: http://orca.cf.ac.uk/id/eprint/115845

Actions (repository staff only)

Edit Item Edit Item

Downloads

Downloads per month over past year

View more statistics