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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 103, 15 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.103 (Mi sigma1185) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Strictly Positive Definite Kernels on a Product of Spheres II

Jean C. Guella, Valdir A. Menegatto, Ana P. Peron

Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos - SP, Brasil
Full-text PDF (334 kB) Citations (14)
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DOI: https://doi.org/10.3842/SIGMA.2016.103
Abstract: We present, among other things, a necessary and sufficient condition for the strict positive definiteness of an isotropic and positive definite kernel on the cartesian product of a circle and a higher dimensional sphere. The result complements similar results previously obtained for strict positive definiteness on a product of circles [Positivity, to appear, arXiv:1505.01169] and on a product of high dimensional spheres [J. Math. Anal. Appl. 435 (2016), 286–301, arXiv:1505.03695].
Keywords: positive definite kernels; strictly positive definiteness; isotropy; covariance functions; sphere; circle.
Funding agency Grant number
Fundação de Amparo à Pesquisa do Estado de São Paulo 2014/00277-5
2014/25796-5
2016/03015-7
Second author acknowledges partial financial support from FAPESP, grant 2014/00277-5. Likewise, the third author acknowledges support from the same foundation, under grants 2014/25796-5 and 2016/03015-7.
Received: June 1, 2016; in final form October 24, 2016; Published online October 28, 2016
Bibliographic databases:
Document Type: Article
MSC: 33C50; 33C55; 42A16; 42A82; 42C10; 43A35
Language: English
Citation: Jean C. Guella, Valdir A. Menegatto, Ana P. Peron, “Strictly Positive Definite Kernels on a Product of Spheres II”, SIGMA, 12 (2016), 103, 15 pp.
Citation in format AMSBIB
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\paper Strictly Positive Definite Kernels on a Product of Spheres II
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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