Work

Strictly positive definite kernels on two-point compact homogeneous spaces

Year: 2015

Type: preprint

Abstract: We present a necessary and sufficient condition for the strict positive definiteness of a real, continuous, isotropic and positive definite kernel on a two-point compact homogeneous space. The characterization adds to others previously obtained by D. Chen at all (2003) in the case in which the space is a sphere of dimension at least 2 and Menegatto at all (2006) in the case in which the space is the unit circle. As an application, we use the characterization to improve upon a recent result on the differentiability of positive definite kernels on the spaces.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1505.00591

Authors: Barbosa, V. S., Menegatto, V. A.

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico

Awards: G176401091, G1987221241, G3572101131, Positive definite kernels and integral operators generated by them, G7840151586

OpenAlex ID: W1754854975

Cites: 13

Cited by: 9

Related to: 10