Extension of the Schoenberg theorem to integrally conditionally positive definite functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:470

Article

Phillips, T. R. L.¹  Schmidt, K. M.¹  Zhigljavsky, A.¹ 

[1] Cardiff Univ, Cardiff Sch Math, Cardiff, S Glam, Wales

关键词: Convexity;    Completely monotone function;    Positive definite function;    Schoenberg theorem;   

DOI  :  10.1016/j.jmaa.2018.10.032

来源: Elsevier

【 摘 要 】

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 T. 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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