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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 117, 15 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.117 (Mi sigma1655) 		 
A Gneiting-Like Method for Constructing Positive Definite Functions on Metric Spaces

Victor S. Barbosaa, Valdir A. Menegattob

a Centro Tecnológico de Joinville-UFSC, Rua Dona Francisca, 8300. Bloco U, 89219-600 Joinville SC, Brazil
b Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos - SP, Brazil
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DOI: https://doi.org/10.3842/SIGMA.2020.117
Abstract: 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.
Keywords: positive definite functions, generalized Stieltjes functions, Bernstein functions, Gneiting's model, products of metric spaces.
Received: June 23, 2020; in final form November 7, 2020; Published online November 19, 2020
Bibliographic databases:
Document Type: Article
MSC: 42A82, 43A35
Language: English
Citation: Victor S. Barbosa, Valdir A. Menegatto, “A Gneiting-Like Method for Constructing Positive Definite Functions on Metric Spaces”, SIGMA, 16 (2020), 117, 15 pp.
Citation in format AMSBIB
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