A Gneiting-Like Method for Constructing Positive Definite Functions on Metric Spaces

被引：0
|
作者：
Barbosa, Victor S. [1 ]
Menegatto, Valdir A. [2 ]
机构：
[1] Ctr Tecnol Joinville UFSC, Rua Dona Francisca 8300,Bloco U, BR-89219600 Joinville, SC, Brazil
[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP, Brazil
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2020年 / 16卷
关键词：
positive definite functions; generalized Stieltjes functions; Bernstein functions; Gneiting's model; products of metric spaces; COVARIANCE FUNCTIONS; SCHOENBERGS THEOREM; PRODUCTS; KERNELS;
D O I：
10.3842/SIGMA.2020.117
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is concerned with the construction of positive definite functions on a cartesian product of quasi-metric spaces using generalized Stieltjes and complete Bernstein functions. The results we prove are aligned with a well-established method of T. Gneiting to construct space-time positive definite functions and its many extensions. Necessary and sufficient conditions for the strict positive definiteness of the models are provided when the spaces are metric.
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页数：15
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