Gneiting Class, Semi-Metric Spaces and Isometric Embeddings

Valdir MENEGATTO; Claudemir OLİVEİRA; Emilio PORCU

doi:https://doi.org/10.33205/cma.712049

Article Details

Gneiting Class, Semi-Metric Spaces and Isometric Embeddings

Authors:

Valdir MENEGATTO | Claudemir OLİVEİRA | Emilio PORCU

Publisher:

Tuncer ACAR

Main Topics:

Probabilities & applied mathematics

Journal:

Constructive Mathematical Analysis 2020 Vol.3 Issue 2, pp.85-95

Document Type:

Article

Publication Date:

5/2020

Document Language:

English

Document ID (Org No.):

2000914189

Frequency:

Quarterly

pISSN:

2651-2939

DOI:

https://doi.org/10.33205/cma.712049

Abstract:

 

This paper revisits the Gneiting class of positive definite kernels originally proposed as a class of covariance functions for space-time processes.\ Under the framework of quasi-metric spaces and isometric embeddings, the paper proposes a general and unifying framework that encompasses results provided by earlier literature.\ Our results allow to study the positive definiteness of the Gneiting class over products of either Euclidean spaces or high dimensional spheres and quasi-metric spaces.\ In turn, Gneiting's theorem is proved here by a direct construction, eluding Fourier inversion (the so-called Gneiting's lemma) and convergence arguments that are required by Gneiting to preserve an integrability assumption.

Article Details

Gneiting Class, Semi-Metric Spaces and Isometric Embeddings

Authors: Valdir MENEGATTO | Claudemir OLİVEİRA | Emilio PORCU

Publisher: Tuncer ACAR

Main Topics: Probabilities & applied mathematics

Journal: Constructive Mathematical Analysis 2020 Vol.3 Issue 2, pp.85-95

Document Type: Article

Publication Date: 5/2020

Document Language: English

Document ID (Org No.): 2000914189

Frequency: Quarterly

pISSN: 2651-2939

DOI: https://doi.org/10.33205/cma.712049

Issues

Authors:

Valdir MENEGATTO | Claudemir OLİVEİRA | Emilio PORCU

Publisher:

Tuncer ACAR

Main Topics:

Probabilities & applied mathematics

Journal:

Constructive Mathematical Analysis 2020 Vol.3 Issue 2, pp.85-95

Document Type:

Article

Publication Date:

5/2020

Document Language:

English

Document ID (Org No.):

2000914189

Frequency:

Quarterly

pISSN:

2651-2939

DOI:

https://doi.org/10.33205/cma.712049