Extension of the Schoenberg theorem to integrally conditionally positive definite functions

Phillips, T. R. L., Schmidt, K. M. ORCID: https://orcid.org/0000-0002-0227-3024 and Zhigljavsky, A. ORCID: https://orcid.org/0000-0003-0630-8279 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

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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:	23 Nov 2024 03:15
URI:	https://orca.cardiff.ac.uk/id/eprint/115845

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