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

Symmetry Integrability and Geometry-Methods and Applications

article

Victor S. Barbosa¹  Valdir A. Menegatto² 

[1] Centro Tecnológico de Joinville-UFSC;Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo

关键词: positive definite functions;    generalized Stieltjes functions;    Bernstein functions;    Gneiting’s model;    products of metric spaces;   

DOI  :  10.3842/SIGMA.2020.117

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown